I've done quite a bit of case reforming and routinely make .30-06 into .243, .22-250, etc, but I haven't done that one. No matter, the principles will be the same.
TRy it, you may be able to do it in a single step with your current sizer. The donor case caliber won't matter because the old neck is going to be cut off anyway. So, use any magnum cases you can pick up cheap until you work out your method. A small collection of .300 WM range brass would be good to start.
Remove the decapper assembly from your .350 sizer, put the body in the press normally. Use a high grade case lube (I like Imperial and Lee) to completely but thinly cover the case below the shoulder. Push the greased donor case into the die in short steps, maybe 1/8" inch at a time, so the case lube can spread over the moving shoulder as it's set back. Remove and inspect the body-to-shoulder transition for an unwrinkled surface. If there are no wrinkles, you're home free (lube dents don't matter, they will blow out). If you have wrinkles, you can try annealing another case down to the proper location of the .350 shoulder and try again. If you get wrinkles on an annealed case you need an intermediate die.
If you do need an intermediate die you can do a web search for CH4D, contact them for an intermediate formimg die; it shouldn't require more than one. OR, if you have a little "grease monkey" in your DNA, you can find a second .350 sizer die and modify it yourself for much less cost. (Home modified sizer dies are all I've ever used for reforming, the factory forming dies are nice but much too costly for my tastes.)
IF I were doing what you need, I'd bore the neck out of a standard FL donor die to make the intermediate. You need to make its neck about half way between the final neck diameter and the shoulder diameter. Find a common, low cost carbide concrete drill bit that's close to the diameter you nieed and use it to drill the case hardened steel die. Drill from the bottom, with the die clamped in a drill press. Eyeball center the bit and push it all the way through, it won't be difficult. Afterwards make a smoothing lap out of a split dowel holding a strip of emery cloth, a medium grit will work fine, to remove the sharp neck edge. Use your "new" die, anneal the necks again and you should have no more trouble forming the .350 cases.
You will have to cut off the much too long neck but it's easy to do that with a Dremel tool with a metal cut-off disc. Use your case trimmer to take it to the finished length. Or, best of all, use a file trim die if you have or can find one.
Now, with your supply of new .350 cases, load a dummy round and measure the finished neck to see if it exceeds proper diameter. If not, fine. If it is too big you will have to turn the necks until they are the proper thickness. Given that you will have thick case body brass in the new necks it's quite likely you WILL have to thin them.
After they have been formed (and thinned?), anneal the necks or they will soon crack in use. Do a web search on CASE ANNEALING to find some help in doing it correctly. Too little heat does nothing, too much heat destroys the needed hardness for a good grip on seated bullets. Any "red glow" you can see in a lighed room is TOO HOT!
All that sounds like a lot of work, and I suppose it is, but none of it's very difficult. So, if you really want to reform cases, that's the way it's done.
