.304" at the lands, .315" at the grooves, should shoot OK with .312" jacketed bullets, but if you are casting for this barrel, then standard 303 British mold which will produce a .313" bullet, power coat the bullet to solve leading and help build up the OD of the bullet, and then size the bullet at .316" for this rig. If with PC coating your still not at .316", then pretty easy to use a cast bullet to polish out the mold to get it throw a slightly larger OD bullet isntead.
https://leeprecision.com/mold-dc-c312-185-1r.html
As for gas checks, you can store buy them, or just punch your own. Hence with powder coating, that will solve any leading problem in the barrel so you don't need a gas check, but may need the gas checks to get the bullet to print well isntead.
Regarding load, unique at max load of 14.5gr (start point of 10.8gr/1300fps as you work up the load) should have be around 1600fps with the above lee bullet PC and sized .316" /.001" larger than the bore of the rig.
And again, you can push a PC bullet well past 2K without needing a gas check even in a rifle, but the glitch with a rifle bullet designed for a GC, tends to not shoot well if the bullet does not get a gas check.
I bring this up, since if you know someone with a mill, not hard to shave the top of the mold to remove the gas check section from the mold, or just ream the GC in the mold to enlarge it instead.
Here is reaming,
https://americanhandgunner.com/modifying-lee-molds/
While this is a lee 310gr GC design mold that the top of the mold was flywheel cut to remove the gas section of the mold so it throws a 270gr bullet isntead.