Hi ushap,
I know what you are going through. I had applied my EAD extension very late and my H1 had alreday expired. Though I was working with same employer, since my H1 expired, I could not work legally after EAD expires. Luckily, I got my case approved before EAD expired.
Now I had talked to my lawyer about it. Its a very prestigious law firm in New York. what they said is after you apply for EAD and get receipt for EAD renewal, your old EAD becomes valid for 240 days automatically. They also said your HR might now know about this, so just don't tell them anything about EAD expiring and if they give you a hard time, we will deal with it.
So I was prepared to do that. I would have taken the risk of keep working there without telling them anything and if they have an objection, I would try taking a vacation.
I think you have advanatage of one month on your H1. You are still using H1 since you never switched on EAD ( never filled I9 form)
I don't think discussing all this with your employer is a good idea specially in these times.
You might want to apply for H1 extension and talk to your lawyer.
As somebody said here, your H1 is valid as soon you get the receipt, you will be good.
Hopefully you will get your EAD also in the mean time.
I think situation is not that bad unless your company ask you not to work after EAD expires which might be a big/remote chance depending on your company.
All the best.