Woodward: If Beartooth is backlogged, Cabellas may have various weights of the gas-checked LBT bullets. I purchased some 300 grainers for my 444s and they shoot just fine. Just make certain you load them to lever action length - which means you may need a Lyman taper crimp die (inexpensive) to seat them to the proper length but not have to worry about using a crimp groove.
Also, the 1:38 twist will shoot gas checked heavy weight bullets just fine. If you log into the Beartooth site and review their literature on the use of the heavy weight bullets you will see that one of their test rifles carried the 1:38 twist and was very accurate with some loads.
Beartooth, as well as Veral Smith, both of who produce the LBT type gas checked bullets for the 44 magnum/444, advocate fire-lapping the barrel for maximum accuracy. The Beartooth information on the results of fire-lapping a 1:38 twist for the 444 makes me very, very happy. I have 3 444s, one with a 26" 6 groove 1:26 twist Montana Rifleman barrel, a Timber Carbine with an 18" 1:12 twist twelve groove bbl and a stock 94AE rifle with the micro-groove 1:38 twist. The last two will get fire-lapped as soon as it's warm enough to get back out to the range.
I don't shy away from using the heavies at all in my 444s - for whatever rifle/bbl/twist you are going to shoot, consider lapping the barrel, and then finding the bullet/powder charge that gives you the greatest accuracy - dang man, that's more than half the fun. HTH. Mikey.