My Winchester 1886 (40-82 cal.) was manufactured in 1887. The rifle is in very good condition but I doubt that the steel in the barrel was designed for smokeless loads. Still, I shoot smokeless so have reduced the loads considerably. All bullets were cast lead Lyman #403169 @ 245 gr. All bullets were crimped in place, Win. LR primers. Powder was IMR 4198, 24 gr. or IMR 3031, 34 gr. or Unique, 14 gr. I have used 1/4 TP wads, tamped down on top of the powder but stopped when I read about how "ringing" of the barrel or chamber could occur from use of wads. Now I use only 14 gr. of Unique and while not a heavy recoil load, it is satisfactory (for shooting at 100 yds.) considering the age and value of the rifle and milder steel of the barrel.
I have experienced something similar to you where the primer ignited but the powder charge failed to ignite or the primer ignited and sent the powder partially down the bore before it ignited (not a comfortable feeling). If the bullet didn't exit the muzzle, it would stick in the barrel and the raw powder ended up in the action during extraction of the brass. These failures of powder to ignite only occurred with 4198 or 3031 and only when I didn't use a TP wad, never with Unique. The second factor and possibly the sole cause was that the outside temp was about -20C (winter in Ontario).
I too, use the expensive 40-82 Bertram brass but have found it doesn't last long due to the thin walls on the brass. Starline 45-90 brass is heavier (from Bullseye Reloading Supplies - Bruno Gross, Fairview Alberta). Trim to length, and run it through the 40-82 dies as normal.
A very heavy rifle but fun to shoot. Keep working with it but be gentle.