@Joedubyk 70g is the general lower limit recommended for mandarins.
I commend you for researching before buying few people do. Your research should tell you, there are a few people in the world who have been successful long term keeping dragonets in small tanks. Off the top of my head I only can think of a few seahorse keepers who have extensive experience culturing live foods and feeding high metabolism picky eaters (the seahorses), who have kept them alive long term in a small tank.
Live food culture is a skill separate and to its own, from keeping aquarium fish and corals. It is extremely labor intensive, and temperamental process. worth investing time and effort into but far easier said than done.
No one is going to say throw a mandarin in a 20gal and whip up some pods in your spare time and it will be fine and easy. or at least no one should, when the ready alternative of just get an adequately sized tank is there.
Just to unpack your own point.
If you consider our actions as hobbyists, "caging these poor lives," why are you asking what the smallest size cage you can use is?
This is effrontery but I cannot help but ask from your posts.
If as you put it you have the "dedication to babysit" it can be done but I caution you it may take a herculean effort.
I do think the blenny would be fine, my friend has 14 fish in a 29 including a tail spot blenny and a pair of clowns.