You had mentioned "I don't see any sign of getting GC by now" does it mean that you have already started the GC process? If your I-485 has been pending for more than 180 days then you could change jobs before your GC is approved and extension of H-1B beyond the 6-year limit is possible. The portability requirements are,

-Your new employment must be in the same or similar occupational classification so new labor certification is not needed.

- Form I-140 has been approved, or is approvable when filed concurrently with I-485;

- Form I-485 has been pending for at least 180 days;

If you meet these criteria and find a new employer then there is nothing to worry about and we can talk more about the regulations in detail if needed. Otherwise chaning to F-1 is an option available at all times.

Good Luck!