You can't ream a standard chamber to an Ackley without setting the shoulder back and for that you gotta pull the barrel. If you had a pull through reamer you could use that and end up with bastardized Ackley/Gibbs case desgine which I think is a very bad idea. I don't see how a rifle could be chambered correctly with quality work and leave the action on.
if the gun is starting to open the groubs up some then here is what I'd do if you jst have to keep the barrel , get a "Tubb's" fire lapping kit and fire lap the barrel , then take the gun appart and send the barreled action off to a goos smith and have him set the barrel back .500" to .750" and rechamber it to the good old 243 , you will have a freash new chamber (better than it was) with a better throat in a barrel that will be smoother than before , in the same caliber that you love and already have the setup to reload.
Personaly , I just get a new barrel and have it chambered for whatever you want (6x47 Lapua) then bite the bullet so to speek and get a set of good dies chambered in what ever caliber you choose (6x47Lapua) and enjoy a new age of shooting.
As for the caliber you can have anything you want (6x47 Lapua) depending on your ranges that you want to shoot. The 6mmBR is a fine round for the lighter bullets , it'll give longer life and has great componets to reload with or if you want maximum range with the realy heavy for caliber bullets a 6x284 , 6mm-06 would work great with the 115gr pills.
I reciently sold a fine little rifle chambered in 6x47 Lapua ,you may have heard of it , its a 6.5x47 Lapua case necked down to 6mm a simple step , you have great brass that will last damnnear the life of the barrel I haven't heard of one that wasen't accurate and will out run the 243 Ackley 95% of the time and do it with less powder !! ,here is a link to a post I just wrote about above mentioned rifle. Notice in the E-mail the ranges that the new owner took his targets at , their are also some guys realy kicking but shooting 600 and 1000yd F-class with this little round.
Long range varmint caliber , 6x47 Lapua !!