Multiple options for 45-70 short.
Hot loaded 45 Colt rounds, 454 Casull or 458X1.5" (458 Win mag cut to 1.5") Belted round.
If you look at the 300 grain bullets the 454 comes very close to the speed of 45-70 out of a rifle. Same as the 458X1.5"
You can make your own, based on a 458 projectile but the 45-70 is a tapered round, not a strait wall so you can not just cut down the 45-70 case to 40mm.
You could use the 45-75 Winchester as a model. It is 1.89" long but a 348Win case cut and necked to either 454 or 458.
Another option, while expensive is either a stunb in 474 Linebaugh or a a Ruger No1. With a 350 grain bullet leaving a handgun at 1500 FPS is more than enough for deer.
Finally a 44 Mag barrel would be the cheapest way with more than enough for deer, ammo is going to be the cheapest of the lot of things mentioned and almost every store you head into will have a box of 44 Mag from 180 grain to 240 being common and custom ordered factory loaded 300 grain hard cast. You will be hard pressed to tell the difference between a deer hit with a 405 grain lead coyboy load out of the 45-70 and the hard cast 300 grain 44 mag out of a rifle. It will be a finger sized hole in and a thumb sized hole out.