U can do H1 transfer and extension at same time.

The new company should be able to file that together for you. Unfortunately I don't know how to fill the forms. PJ may know. Keep EAD at hand in case you don't have enough time.

Also, use of EAD is almost equivalent to H1 at 7+ years. Why you want to keep H1? The loss of 485 will also nullify your H1 at 7+ years, since this H1 extension is based on a pending GC application.