i think indian companies will be best bet for you to maintain your status
once they transfer to theirs you will have time to look for job yourself otherwise they can market you too.
i am also  in same case like yours
i have found many desi interested in transfer but i think its better to start the GC process so that we won't have to go through the same case again
i also did some interviews and waiting for their results but i am going to stick to H1 though but i am also planning to get sth with 2 weeks n have been out of job for 2 weeks like u