Re: what cal for a elk Handgun????
Sure, you can build a "handgun" on the target action, with at least a 16.5" barrel and over 26" overall.
My suggestion. Get your action, a 18" barrel in something like a 338 edge or 300 WSM with a brake, and a good scope, bases, etc. Lots of options.
An easy startingpoint is the Choate Ultimate Varmint Stock, cutting off the shoulder stock. No bedding required. I think its made for the action.
Thats a long shot for a rifle, much less a shorter instrument. Practice a lot.
Ask for 358hammer over a specialtypistols.com.