"...Trapdoor Springfield should only be shot using lead cast bullets..." Isn't true at all. Factory ammo has been loaded with jacketed bullets to BP specs for eons.
It is, and it isn't true, exactly. It's a difference between what the Trapdoor (originals) can be shot with, and what people feel they
should be shot with.
Jacketed bullets loaded with modern smokeless powders (to Black Powder pressure specs) are "safe" to shoot, but there is a significant segment of the old rifle collectors and shooters that feel they should not be used.
Remember the "steel" in the old guns isn't all that much better than iron, and NOT close to modern alloys. It's a fact that jacketed bullets wear a barrel faster than lead ones, and with "softer" steel, it is even faster.
Also there is evidence (not proof, as far as I know) that the old guns fail at a higher rate when shot with smokeless ammo than they do with black powder loads. It is believed that while the smokeless pressure is within limits the difference from black powder puts a different kind of stress on the gun.
Now, .45 pistol bullets in a modern gun, like one of the Marlins?? Ok, can be done, but not without taking some extra effort AND using the right bullet.
First issue, the difference in the nominal bore and bullet size, the rifle is .458" .45ACP and modern .45 Colt bullets are .451-452", older (pre WWII) .45 Colt goes .454".
I suggest you research "paper patching".
Next issue is use in the rifle. Auto pistol bullets don't always have a cannelure to crimp into, and running non-crimped ammo through the tube mag is a good way to get bullets pushed too deeply into the case. And then, there is feeding, which you would have to experiment with.
I would think the best way would be to single load them into the chamber.
Also, I think it would be a poor idea to try and push something like a 230gr ACP bullet to high speeds. If you want that, use a slug properly sized for the bore.
In other words, I don't think the effort to make .45 pistol bullets work is worth it. My "reduced load" for my .45-70s (currently down to a Ruger No.3 and a T/C Contender) is a 385-400gr cast slug and 10gr Unique. Not sure of the velocity, its low. But is accurate in my guns, and very light recoil. (filler recommended for non range use)