OK, lets clear up a few things....
When writing about caliber, including cartridge names, using standard English decimal system, it is proper to put the decimal point before the number (.45-70). When using metric measurement, do not put a decimal point at the beginning, only use it if it is somewhere in the middle of the name. (7mm Rem Mag, 7.62x39mm, 9mm Luger, etc.)
When talking about bullet weight in grains, do not use the decimal point (405gr, 500gr, etc.)
The confusion is that there is a 405gr .45 caliber bullet, and also a .405 Winchester cartridge. And, while the .405 Win is about half an inch longer than the .45-70, a quick check of case specs looks like it would possible to put a .405 Win into the chamber of a Trapdoor. If it is possible to get a .405 Win in there, firing it would be a disaster!
The .405 Winchester is a long straight (essentially) rimmed case, smaller in diameter at the front, than the .45-70
bore (so the longer case would extend beyond the chamber into the barrel), and with a rim size of .543" compared to the .45-70's .600" rim. So I think it would "chamber". The question then is, would the .405 round be held in the right place so the firing pin could set it off? I don't know, and don't have the ability to physically check. In any kind of repeater, the greater length of the .405 Win would keep it from working
Its a very, very, very BAD IDEA, even if it is physically possible, so its something to be careful to avoid. The .405 Winchester was made to launch a 300gr bullet at 2200fps, so firing one in a gun not made for it is high on the list of things NOT TO DO! "Warning! Danger! Danger Will Robinson!"
Sorry if I been to be harping on this, you probably aren't as confused as I think I am...
There are lead bullet 405gr smokeless powder loads available, (or at least as much as anything is these days
), which would be the best ammo for you 1889 Trapdoor, if you don't care for using black powder. The 405gr Jacketed ammo is fine, but be aware some people claim it will wear the rifling faster than lead bullets. The old barrel steel wasn't made with jacketed bullets in mind. That being said, I know of one original Trapdoor that was used for a decade in cowboy action side matches and shot a lot with JSP bullets and never had any issues.