Sounds like a bad battery to me, too.
If you simply "hot wired" the marine battery to the starter relay, but left the bike's main +/- hooked up to the bike's battery, it could simply be that the bike battery doesn't have enough guts left to run the ECU, fuel pump, injectors, etc.
In other words, enough voltage to read 12.xxV, but not enough reserve amperage to run the bike, even if another battery is running the starter.
Take the +/- cables off the bike battery, hook em up to your marine battery and give that a shot. Just pretend that your bike battery is toast, and get the bike running off the marine battery.
The good news is, assuming you wired up your amp-probe correctly, it looks like your starter is fine. 31 amps full-load test is excellent.
However...(gawd I hate howevers) this bothers me...
Scenario 1 using current MC battery:Reading at Battery at rest: 12.3 Volts
Attempting to start, reading on wire from battery to relay: ~31 Amps
Attempting to start, reading on wire from relay to starter: ~31 Amps
Result: Click click click on relay, no starter movement
If the starter doesn't run on Scenario 1, where is this 31 amp draw coming from???
Back to my suggestion above...remove the bike battery completely from the equation. Hook up the +/- leads to the marine battery and crank that bitch up. Please give this a shot. Oh, and to eliminate ANY over-fuel issues from being dicked with so much, when you do attempt your next "crank" session, do it with the throttle held wide open to assist in a possible flooded situation. Just hold the throttle WFO, crank, and hold till the bike starts up. Let off the throttle and let the bike warm up to four bars on the temp gauge before shutting down.
Keep at it...you'll get this worked out, without dealer intervention.