This purely depends on how much you can rely on your new employer. If you do rely on them then you can have your H1 transfered, start working with them and then get your LC and 140 refiled. You would be able to retain the original PD of April 2004, as long as the old employer does not retract your 140 (Or so I read on other forums related to this topic).
The pitfall is, if your new employer gives you problems after you join them and cause problems in filing for your LC and new 140, you will be in big time trouble, as you will be left no where.
LC: PD:08/23/2002 45D: 11/2005 AD: 04/18/2006
H1 7yr Ext:10/2005
140:FD:06/28/06 RD:07/10/06 PP:11/30/06 AD:12/04/06
Moved on to Company B:
H1 valid until: 12/2009
Company A: Agreed to process for future emp
485:RD:07/02/07,ND:09/08/07, latest LUD:04/07/08
EAD:AD: 10/01/07 Cards rcvd: 10/05/07