25-06AI headspace?

Suggestions on the technique for polishing down the top of a shell holder should it come to that (I would definitely do the holder and not the die):

Put the abrasive sheet on a piece of glass, the thicker the better. Glass, unless it a really old window (say 1930's or older), is remarkably flat. It is not as good as a true surface plate, but it comes darned close. A thin smear of grease will usually keep it from moving on the glass.

Move the shell holder (or whatever) in a figure 8. Periodically rotate it under your finger. You're much less likely to make it lop-sided than if you just go back and forth or in a circle.

The tool and die machinist that taught me this process called it "Scooting"; for what that's worth.....
Your die probably is too long and just not reaching it. You can try redding shell holders if that doesn’t work then shorten up your die. I’ve done it in past with belt sander best with lathe. As long as your factory 25-06 chambers your good.
The Redding shell holders are LONG, not short. They are in like .010 increments longer to allow for less push back of the shoulder without "guessing" by setting the resizing die back with the locking ring. I wish redding made a short set too, for this reason. OP has the opposite problem -- cannot get to the shoulder.

Agree that taking material off the shell holder is the way to go. Get a plate glass shelf from Home depot or Menards. Thicker than window glass. Use spray contact adhesive to attach 220 or 320 wet/dry paper. And here's my tip: Use WD-40 for lube, not water. Seems to keep the metal in suspension better.
By taking metal away from shell holder your taking chance of breaking lips off shell holder and sticking a case in your die. Make sure to use enough case lube. Id take it from the die personally but then again i got a lathe. .002 off the shell holder is a lot. But off the die its not much. Ive done it with a grinder in a pinch and its still working flawlessly. I just do it in lathe when i can if i have too.
Maybe if we we talking .05"+ of metal removal. For ~.01" or less I don't see a problem as that won't even remove the factory chamfer. Scooting that much metal off will take a while.
Based upon what you have written for dimensions on your brass prior to and after fire forming I suggest taking .003 thousandths off of the top of the shell holder. I have read some of the replies here, this is how I have and how I would do it. First I would take a micrometer reading of your shell holder to use as a base line. From there I would use a flat surface such as a piece of glass on a work bench and a sheet of 400 grit, wet sandpaper and some WD 40 or other thin oil (Rem Oil) to use as a lubricating base on the wet sandpaper. I personally use the metal top of my bench saw as a solid base. From there put a generous amount of WD40 on the wet sandpaper, grasp the back of the shell holder between your thumb and trigger finger and make a figure 8 on the sandpaper, use your other hand to keep the sandpaper from moving. The longer the figure 8 the quicker the top of the shell holder will be removed. Shell holders are made of hardened steel so metal removal is a little difficult, but very doable. After a few swipes across the paper, clean the shell holder off and take a micrometer reading. Keep repeating this process until you have removed .003 thousandths off the top of the shell holder. Remove more off the top if you want to increase the shoulder bump more. Try resizing some cases using the modified shell holder to see if you are reaching the desired measurement. Sometime you may have to remove one or two thousandths more off the top of the shell holder due to spring back of the brass. Also different brands of brass may give you different measurements due to spring back. Annealing prior to resizing will help to prevent the issue of spring back. Also you could have something as simple as a messed up, oversized shell holder and no real problems at all other than an $8 shell holder. So... you might want to start there????? With today's market "supply and demand" and "quality control" are no longer synonymous, nor ought not be used in the same sentence anymore!!!!!
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I have thinned down at least a dozen shell holders over the years. I take off .006-.012 to eliminate the "caming over" of the Rock Chucker press. Since the bottom of the sizing die never touches the top of the shell holder if you have taken off enough, canted top shell holders are not an issue, within reason. Shell holders are hardened, using sandpaper is a tedious process. I have a fine wheel on a 6" bench grinder, and very gently hold the shell holder up against the side of the bench grinder, carefully with little pressure. I dip the shell holder in a cup of water frequently, then measure with a pair of calipers. Always wear safety glasses and/or face shield when using a bench grinder.

You will have to take .035+ off the top of the shell holder before the shell holder becomes useless, so just measure the shell holder thickness frequently with .003-.006 removal off the top being sufficient. The most I have ever had to take off the top of a shell holder is .013 for rifle cartridges, Lyman, RCBS, and Forster which is a deep subject in and of itself. I was trying to make a sizing die work that was reamed too large, so production dies do vary in size.

Only one shell holder did I have to grind down thin on the top and that was to size the bulge out of 40 S&W brass or take more bulge out.

Taking the material off the bottom of the Die is a really bad idea, for many reasons, and is ill advised.

CBuck516, you have another problem with your 25/06 AI, and that is using Lapua brass. Many do not understand that European Brass is made to CIP spec and American brass is made to SAAMI spec, in some cartridge configurations. The CIP spec brass is often larger in the web, just in front of the extractor groove, and often this brass simply does not work in the SAAMI spec chambers. So this means that Lapua, Norma, and RWS brass maybe too large in the web to be used in your SAAMI spec chamber. Chances are that if you Change to Winchester brass, new Lake city Match '06 brass, or Remington brass, your problem will be solved. However, we do like to use the best brass when we have that option.

I ran into this exact same problem with Custom Chambers in 223, 22/250 AI, 243, 243 AI, and 22-243 AI. Factory chambers are much looser and Headspaced longer than Custom barrel chambers as a rule of thumb, which explains why some std calibers in Lapua brass can be used in factory guns and NOT custom..

If you are dead set on using Lapua brass in your 25/06 AI, then a gunsmith can remove the barrel, put it in the lathe through the headstock, and "polish" out the chamber a tad. SOME gunsmiths have CIP and SAAMI spec reamers, and PTG and JGS Reamer makers are familiar with this problem.

Question: Your Lapua New brass Web dimension on the Lapua 30/06 brass is___________,
New Winchester Web dimension is .465, which I have on hand

while the fire formed Lapua brass web dimension is__________,
and the Full length Lapua sized web dimension is__________.

Taper on the AI case is very little, and you may not achieve the dimension in the web you are looking for by removing metal off the shell holder and your darn sure will not get there by taking material off the bottom of the Full Length sizer due to the body taper involved.

On some AI's, I have cut the bottom off of a Small base sizer of the parent case, ending up with a "ring die" that is only about 3/4" long to size the bottom of the case only. These ring dies are complicated and expensive to make with sometimes less than desired results. Other options give a more harmonious outcome, like Winchester brass. A carbide-tipped cut-off blade used in a lathe is needed for cutting off the Hardened full-length sizer. Having your gunsmith make "ring dies" is a mess to get involved with just to obsess over having to use European brass, but I have done it on more than one barrel, and it is ill-advised.

CBuck516, if you measure the web dimension on new Winchester brass and New Lapua, you are going to be in for a real shock at the difference in dimensions with the Winchester being MUCH smaller, eliminating jumping through any hoops on the issues of shell holders, ring dies, gunsmith polishing out the chamber, etc.