If your spouse's H1 status is still valid, you can go outside the U.S. and apply for a new H4 visa and come back. Then you will be in H status again. But then you can't keep your job, unless you don't want to keep your H4.
In another word, for H4 holders, work under EAD, lose your H4, or keep your H4, but don't work. Choose from either one.