Hamachi is allowed for co-op speedruns

Like the others said JellySquid is the original author of all three mods, the team managing them recently rebranded to CaffeineMC, so the option's been changed to that now

Moving the mods under an organization had been planned for awhile, in part to make managing permissions easier, but also to reflect the fact multiple people are contributing to and maintaining them.

I believe the team have allowed people to restart their game if it's unplayable for one reason or another, so there should at least be a chance of getting it accepted. It would help if you were doing desktop capture and the crash actually showed if it's a really good run, otherwise sending them your .minecraft/logs and .minecraft/crash-reports folders would probably be enough if you open a ticket on the discord.