vistaptb

Maybe this has to do with the heroes' alter egos? The Green Arrow is Oliver Queen, and it's hinted at in the first stanza. Norman Osborn has 12 letters (a base for one of the exponents), and Britt Reid has 9. However, Oliver Queen has 11 letters, and none of the numbers given is 11 raised to the power of anything.

I thought the word "power" denoted superheroes, but then I noticed this: 6436343=23^5, 248832=12^5, 104976=18^4, 59049=9^5 or 3^10, 38416=14^4, and 15625=25^3 or 5^6. Sorry, I just looked up Green Arrow, and it's a much better answer than Green Lantern. I think the key to this is to find the "normal case" for each superhero, whatever that means.

I'm thinking stanza 2, line 3 might refer to the Green Lantern, going with the superhero theme. I'm guessing that since there are only 3 keys and the first stanza seems more mathematical, it gives us a clue to encrypt the words of the other three stanzas to make three of the numbers on the Venus fly traps. Bloke's a reasonably common word in American English, so I think it's just there for rhyming purposes.

Adding Y-san's hint, here is a list of the forced moves we have so far.

Yeah, you're right. I guess I missed that. It's nice to see a puzzle where we can understand the rules, though.

A few additions to the list. h7-h8 a4-a1 a3-a2 f8-g8 c6-e6 b6-a6 g6-g7 b7-f7 f1-f3 c3-b3 d4-c4 d7-d5

Numbering the squares like those on a chessboard, I've put together the following links: h7-h8 a4-a1 a3-a2 f8-g8 c6-e6 b6-a6

I like DudleyDude's answer, but since Y-san hasn't posted yet, I'd guess that we're looking for something more. So,

Or we can apply the numbers=chemical symbols pattern to the color of the door (346291), which yields SeSmPa as a code.

BASTE (which I'm pretty sure is right) would make it 334453.