You need be hurry

If you can get your application receipt before your H1 expired, everything is fine. If not, you may have a little trouble. Your new application may be rejected based on this reason. And you cannot work before your new H1 approved. You need to tell the international office and push them often. I almost called them everyday last year when I extensed my H1 or they can let my application sleep there for 2 months.

Suggestion: you may need a vacation before you get your new H1. You must let your boss to apply premium process, so you can get it for half month after you submitted them.

Good Luck.