In looking over the customs threads, I notice that a lot of mods can be made using Gundam parts plugged into the limbs of MMS figures in lieu of the normal Busou Shinki armor parts they come with. Does anyone know if there's a male figure or line of male figures out there that can be modified in a similar way to make them into a "Armored God Prince"?

While I'm sure there's something out there that could be made to work with some modding and 'bashing (perhaps a male figma base), none of the main mecha musume base bodies you'll see used around here (specifically, Busou Shinki, Bandai's AGP, and Koto's RAcaseal kits) have male equivalents. The genre is "mecha musume," after all.

That's what I was getting at; if there was a line of figures out there (like figmas, I guess) that produced male characters who could substitute functionally for an MMS body. i'm just not savvy with all my toy and figure lines yet.

there are some 1/12-ISH Halo kits from Bandai that you could start with if you want something more human, but they'd need a lot of work. If you don't care about that and just want a male-proportioned base, use Frame Arms and give them headswaps (which the Halo kits would need anyway)

There's already been a similar equivalent from Konami called AM Driver, which is arguably a direct predecessor to Shinkis. Frame Arms is the currently the closest equivalent.

...Owning several items I'm really not sure how I forgot about AM Driver.

Those are probably the best bet as they're directly compatible without mods with most shinki parts; the only ones that won't work would be the ones that modify the base body...