From a gun smithing point of view There are good choices of actions, and there are bad choices.
Rifle barrels for the 500 might also be a problem getting because of the bore diameter.(.4880) and (.4983 groove diameter)
A good smith can build most any action/barrel/ cartridge combination. The difference is cost.
If you pick poorly it may cost a lot of money .
I have built rifles with rimed cases and found that there are several actions that are not suited for this application.
Any bolt with a recessed face (Push feed) requires extensive machining And possibly a new extractor
installed.
Controlled feed actions are better suited for rimed cases and single shot rifles are best for this.
If you want to hunt with it, an 1885 high wall or a Ruger #1 (Or any break open action) would work the best.
Rimed cartridges are Problematic in repeaters unless they are designed for them.
With the large case head (.560 ) a falling block action is what I would recommend.
J E CUSTOM