Shoot the crap out of it (in a controlled manner)
This seems to be a case of, literally, "shoot the crap out of it".
The bore appears to have sharp-edged pitting. A Garand or .30M1 carbine demonstrates very nicely that a clean hole that is very short, compared with the bearing length of the bullet, will not harm accuracy. But rough edges on the pits tear up the surface of the bullet, thus leaving the residue that you observed. And, as you shoot more and more, the pits become clogged up and the edges of the pits are smoothed off - just a smidgeon - and thus the performance improves a wee bit. You are indeed, "shooting the crap out of it".
However, to save yourself time and the expenditure of hundreds of rounds, may I very seriously suggest that you apply "fire lapping". (described some time ago, please search it out yourself). This will take the sharp edges off the pits and can improve performance to the point where you have an acceptably shooting rifle again -and saved a barrel that looked like it was destined for the scrapyard.
But until you have done that, all musing about loads, bullets, draws etc etc is (guys, please excuse me) an academic waste of time.
Just my 10c-worth of course, but i've Been There and Done That on a Winchester LAR, a Brazil Mauser and an Artillery Luger.
It works - do it.