No you cannot work in between EADs. If you have used you EAD and are not on H1 anymore, then you will always have to have a valid EAD to work.
If you do not get your new EAD before your current EAD expires then, you cannot legally work. Even if there is one day gap between two ead's you cannot work that one day.
you may want to talk to your employer, and work out some sort of a deal. You can tell him to pay you a bonus later, and not pay you while you don't have an EAD. Be advice, this is not exactly right, and I do not support or encourage this way. Talk to your lawyer.
The best you can do is apply for a new H1B through your current employer with premium processing, or go get interim EAD after 90 days from the date of your EAD application.
