well, tell your lawyer that the USCIS sometimes does that and causes us trouble. it is not your fault that they gave you an H1B before J1 waiver approval. it is their fault and unfortunately, there is nothing one can do to emphasize that.
main thing is to clarify from DOH what dates they are going to put down for your J1 waiver and what you can do if you are short. this will come up when you apply for your greencard because you are going to have to show 3 years. it all depends on whom you get from USCIS reviewing your application, becoz if it is a nit picker who counts the days, then you will be in trouble. you want to be on the safe side and make sure you have your dates. from what i understand, DOH also sends a letter to USCIS with the dates of your J1 waiver. i don't know if USCIS ever goes back and checks that. but then, we have no control over what USCIS does or does not do. all we can do is make sure we have what is required.
these guys just make our lives miserable.