/remake is available if you have had a player disconnected for at least either 1:30 or 2:00 at the 3 minute mark.
I believe the way the First Blood thing works is If YOUR team gets first blood it is unavailable, but had our jg invade and kill the enemy jg at 2:30 and get first blood and still been able to remake.
But on the other hand I had one of the most fun, stomp games as supp Lux when the enemy ADC was disconnected and their supp morgana was tired of remaking so she let me auto her and she tower dived and gave me first blood. The enemy team was unable to remake due to it. I don't know how it works specifically on the first blood, id submit a ticket or something