Verizon’s locked bootloader on their Galaxy S III hasn’t stopped development at all to this point. Two unofficial ports of AOKP and CyanogenMod 10 popped up, with each either being as close to fully working as can be or with a couple of minor bugs that are currently being worked on.
AOKP Milestone 6 appears to be ready for release and a daily driver without any known bugs so far. CM10 is currently still being referred to as an “alpha”, however, data and all the other most important core features are working. You may just want to look into either one of these, especially CM10 as they always do a outstanding job and go beyond the call of duty.
These ROMs are only possible thanks to CVPCS’s kexec boot sequence and will appear to boot twice during the bootup process. That’s all normal and is just the kexec doing it’s work.