I have a Maarlin camp carbine in 45ACP that I have shot a couple deer with under the limitations you have set for your self.
It went pretty much like this, Bang, plop...dead deer. Both were 140 ish pounders shot at under 50 yards. Shot at the base of the neck/high in the shoulder. Using Remington Golder saber 185gr+P ammo.
Your load will penetrate better, but even I had full penetration at that range. You will be fine. Bullet placement and calm animals is key.
Good luck, post up how it goes!!
CW