If the client is offering job then perhaps you can be direct hire there and work with H-1B for couple of years before initiating your green card. For green card, you can then use the earlier experience, worked at consultancy (official employer) to justify the necessary skills sets obtained before joining this company. Or just find a new employer all together & move cities etc. to start fresh if you've the necessary skills now.

No point, sticking to a Desi consultancy if they're playing bad with you. Good Luck.