Mike, I have used thin jacket bullets in many damascus rifles with no discernable problems. I find most rifles are easier to regulate with jacketed bullets, and they seem to shoot very well in Henry rifled barrels. I have put hundreds of Woodleigh 650 gr BPE bullets through my Ca. 1895 steel barreled Gibbs double at 1850 fps. After years of messing with paperpatch, hard lead, soft lead, 3031, black powder, etc; Graham Wright's nitro for black load[Shooting the British Double Rifle] put the 650 gr. Woodleighs in the same hole at 50 yards. When was your Adams made? I believe that there was a 520 gr load used in the 1870's. Are you using black or smokeless? Most express rifles are easier to regulate with 4198 than black, and the presures are lower.
All the best, Mal