If you bend the rammer by using .400 diameter soft lead balls, then your revolver is a poorly made piece of junk.
I use .380" balls all the time, as do many others, because the slightly larger ball (over the recommended .375" ball) not only stays in the chamber better, resisting movement from recoil, but also provides a wider bearing band for the rifling to grip.
In my own Colt 2nd generation 1851 Navy I've used balls as large as .433 inch, without damage. The lead is soft, the chamber mouth cuts into it easily.
No, I didn't notice a marked improvement in accuracy using the .433 balls, so I returned to the .380" ball.
Without knowing the quality of your revolver -- and there are some truly abysmally made ones out there, especially those made with brass frames -- I cannot recommend using .400" balls. I'd have no qualms using such a size in my Colt Navy, but then the Colt is an exceptionally well-made revolver.
Search the net for casters that offer .380" balls of pure lead. A large, well-stocked black powder shop may have some, cast locally.
I've written Hornady and Speer many times about offering .380" balls commercially. No reply. Seems to me, they're missing a market.
Anyway, I can't recommend .400" balls -- but only because I don't know whether your revolver is well made or junk with poorly tempered parts.
Don't bother with tapping .38 or .357 Magnum bullets for your cap and ball.
Cap and ball conical bullets require a reduced step to start into the chamber, so the bullet may be seated straight. Lacking this step, known as a "heel," it's nearly impossible to keep the bullet straight as you try to seat it.
Bullets seated crooked are inaccurate.
I've been shooting cap and ball revolvers since about 1970. Tried all kinds of projectiles through the years, including bird shot with felt wads, and I know what works and what doesn't.
Lee makes a very good bullet mould with a heel, designed for .36 or .44-caliber cap and ball revolvers.
Use the Lee .450 mould for most .44s, and the .457 model for the Ruger Old Army. This is why Lee makes moulds for two different sized bullets.
Dixie Gun Works sells conical bullets of authentic design, cast by their employees.
Conical bullets must be stubby, so they can fit in the small space under the rammer. For this reason, modern lead bullets are often not useable.
Black powder bullets must also be cast of pure lead, or nearly so, and contain a relatively moist lubricant that is not based on petroleum products. Bullets intended for smokeless powder reloading are wholly unsuitable because of the lack of a heel, bullet length, alloy and lubricant.
Gad Custom Cartridges sells balls and conical bullets for the .36 caliber:
Conical -- 105 gr., 100 for $8.00
Ball, .380" -- 100 for $6.00
Lots of other bullets and loaded ammo for old guns in the same site, too.
I think you'll find balls much easier to use and load. Were I you, I'd buy 100 conicals and a few hundred balls. This would set you up for a while.
Search the internet for my old post, "Proper Use of a Cap and Ball Revolver," and "So You Want a Cap and Ball Revolver." These two posts, created about 1999 and updated through the years, will give you a ton of info.
Enjoy that Remington .36. I have a Pietta Remington .36 and it's a fun shooter. Not nearly as accurate as my Uberti-made Remington .44, but the .44 is uncannily accurate. With my Pietta .36, I get 4 inch groups at 25 yards from a benchrest, with an occasional 3" group.
My 58-year-old eyes are probably to blame for much of this.
Have fun. Wear hearing and eye protection.