Hodgdon uses a .308" dia. bullet because they don't know what country of origin your Mosin rifle you plan on loading for comes from. The Finnish Mosins as well as the American contract Mosin rifles can have groove diameters that are .310" or smaller so the .308" dia. bullet is a safe bet but depending on the dia. of your bore it may or may not be as accurate as one that best fits your bore. Have you slugged your bore and if so what is the groove to groove dia.?
Sierra makes several .311" dia. ProHunter bullet in various weights 125,150,180 as well as the 174 gr. MatchKing BTHP. Speer,Hornady,PPU,Barnes as well as a couple other all make bullets in the .311" 123 to 125 gr. range,take note that most if not all the 125 gr. or lesser weight jacketed bullets are designed as hunting bullets for the 7.62 x 39 an should only be use on light game and varmints if you plan to hunt with them otherwise use the 150 or heavier weight SP bullets for larger game.
As for the Sierra .311" 125 gr. ProHunter the Lyman #49 manual listed load data using Varget as
45.5 grs. starting load at 2677 FPS. and a Max. load of 50.5 grs. at 2994 fps. your results may vary,OAL is 2.800" with the 125 gr. bullet. I personally shot that bullet quiet a bit in the old days and I use the starting load of 46.0 grs. Reloader #15 and found it to be very accurate,I was bouncing an old softball around at the range at 100 yds. off hand using the factory sights with no problems with no real felt recoil using the light weight jacketed bullets,even the heavier 150 gr. .311" handloads are nowhere close to some of the LB and HB ammo as far a felt recoil goes. You can also take a look at The Load by Ed Harris which can be use with the .308 to .311" dia. bullet as well using 13.0 gr.s of Alliant Red Dot
http://www.hensleygibbs.com/edharris/articles/The Load.htm
I can sympathize with you as I have a bony shoulder where the butt plate sits and the Bulgarian surplus HB ammo beat it up pretty well the LB ammo was OK. If you need a good recoil pad I would highly recommend the HIVIZ slip on pad it fits the Mosin rifles like a glove
http://www.hivizsights.com/product/slip-on-recoil-pad/
Although I have several tins of good Russian an Yugo Surplus 54r ammo as well as several different jacketed bullets I can load for my Mosin rifles,I'm saving those for a rainy day as it can't be replaced for what I paid for the ammo and component bullets years ago. I've pretty much just shot cast lead in them for the past several years an had excellent results with 90,160,185 gr. as well as a new mold I had Tom over at Accurate cut for me to fit my deep throated 91/30 that drops a 215 gr. FN bullet. For the most part I use Bullseye for the 90 gr. sub loads and 2400 or H4895 reduced loads for the heavier bullets,acl864 can attest to how well those loads shoot.
With cast loads in the Mosin rifles which have a 1:10 twist bore same as the SKS using a cast lead bullet in the 160 to 200+ gr. range you Velocity/RPM/accuracy threshold is going to be in the 1800 to 1900+ fps. range. Cast bullets are not perfect even though they may appear so an are not constructed like jacketed bullet so they are more substitutable to the rotational forces imparted on the bullet that causes instability as it is launched into the leads as well as those imparted on it by the rifling. At some point along the load development way with cast loads as the velocity increases so do the RPM's imparted on the bullet by the rifling an the bullet begins to be distorted by those forces. With cast lead one can easily reach jacketed bullet velocity within reason simply by using a slower twist bore like the 1:14 to 1:16 twist cast bullet benchrest shoots use. But even with the limitations of the 1:10 twist bore on the Mosin rifles excellent target,plinking and hunting loads using the right bullet or cast lead bullets can be easily assemble.