I saw some pics of that falling block you mention.
FWIW Connecticut Shotgun Manufacturing made a rifled 20 ga double that was only 3500.
RBL professional I think they called it.

But a .44 mag double, for in the woods....just seems a great match.
Cheaper to just get a Baikal .45-70.

Thankfully none have been at any gunshows I've visited.