Maybe it's possible to improve the performance by using a Wonderwad wool Bore Button between the bullet & the powder to work like a gas check, to prevent some of the gases from blowing by and to help prevent accuracy robbing fouling in the bore, especially since you're getting good accuracy for a couple of shots.
But while some 1 in 48" twist barrels will satisfactorily shoot the long heavy concials like the 370 grain Maxiballs, these bullets may just be too long to be well stabilized by that medium twist barrel. That's just my gut feeling.
I would suggest that if you want to shoot a bore size conical, that you select a lighter and shorter one, it should stabilize better. It appears that TC makes conicals in various weights and IMO, stay under about 300 grains.
There is a 275 grain TC .50 advertised:
http://froogle.google.com/froogle_u...pFDAMPDxWUvtxQUCnjpxGNwAAAAAAAAAA&gl=us&hl=en
And 255 and 240 grain .45 caliber TC conical's that you can try to use with the right size sabot for .45 caliber bullets, (not the .427-.430 sabots, they won't work with .45's).
http://www.midsouthshooterssupply.com/item.asp?sku=000307794
http://www.midsouthshooterssupply.c...t2=COMPONENTS&dept3=BULLETS ONLY&dept4=45 CAL
Any lighter, shorter sabot/.45 bullet combination may work satisfactorily, and the 255 grain .45 maxi hunter has shot well for me out of a 1 in 48" twist barrel. A 245 grain bullet/sabot is one of the most popular bullet/sabot combinations.
And you can always try a patched round ball too. That's something that really won't shoot well out of a fast twist inline. And you can plink more accurately at moderate ranges without needing to swab as much if using a well lubricated patch and lower powder charges with your Grey Hawk.
More shooting can sometimes equal more fun.
Plus, the lighter projectiles won't produce as much recoil.
Why not try out more bullets until you find one that you like. There's also a 250 grain .45 REAL bullet and a 250 & 320 grain REAL in .50.
This outfit may let you mix and match bullets within an order. I've never shot the REALS but some folks like them.
Good luck and let us know how things work out.
http://blackjackhill.com/zencart/index.php?main_page=index&cPath=1_6
http://www.leeprecision.com/cgi/catalog/browse.cgi?1162544960.4931=/html/catalog/blackpow.html