This is a very tricky situation. If you F1 is approved too early, you will get into trouble. CIS may ask you to go outside US to get F1 stamp.
Some people say you need to keep your H1 by working the day before your F1 program starts (effective date on I20).
Some people say you need to keep your H1 by working the day before your F1 program starts (effective date on I20).