1) Get the offer
2) You have 3-month H1-b visa? Your hobby needs a sponsership from his employer to get a new H1 or transfer his current one. The "big" firm may think your man does not need H1. right???
3) Find a lawer to help you on Green Card. $3000 ~ 5000. It is worthy.
4) After filing I-485, you will be eligiable to apply an Advance Parole (Hui2 Mei3 Zheng4)
In addition, my wife went to Canada (for business)withh H1 visa after our filing I-485. No any side-effect occurs afterward.