You can definitely find a new employer who is willing to transfer you to their company and so can file for H1B Transfer. They can even file for your H1B Transfer right now, given you have your Approval Notice or atleast Receipt#. You don't even need your pay stub to do this. 

Also, you don't need to inform you H1B petitioner about your transfer plans, once you receive your receipt notice from a new petitioner it won't matter even if they withdraw your petition.

Hope it helps. Good Luck!!