How do you know H-1 cannot study Full-time?
If you work full-time during the day, of course you can study full-time.
I am a H1 and go to school part-time. I never heard that H-1 cannot be a full-time student at the same time.
Check International student offices of different schools. I think some school's ISO are very bad and the person there are extremely unfriendly/hostile to people without a GC. Be careful not to be tricked by these bad people.