Provided you completed the 1040-X properly (and I'm guessing you did), and the IRS shows it as having been received, the IRS already understands that you want to go from MFS -> MFJ.
To correct something
@reeshau said, you are not supposed to include a copy of the original return unless required for some reason to do so - this is mentioned at the end of the instructions for Form 1040-X on the IRS website.
The IRS amended return status probably still says it's being processed because the IRS is waiting on you to complete and return the requested information.
The IRS does move slowly these days - they are overworked and understaffed - but in general they get it right most of the time and the best thing to do (most of the time) is comply with their requests, be patient, and check back if you haven't heard about something in the promised time frame.
In your case, I'd complete the paperwork the IRS is requesting and send it in. Until you do, I expect the IRS has just put your 1040-X in a "pending taxpayer correspondence" status and nothing will happen.
I'd read the notice carefully several times and do what it asks for.
The only reason I can imagine that they sent the MFS back for you to sign is that a tax return is not valid unless signed. So even though you shouldn't have needed to send the original return in, the IRS agent may have just reflexively thought about that rule and required a signed copy.
Questions:
1. Did you and your spouse e-file or paper file the original returns in January?
2. If you paper filed, did you sign the originals that you sent in January?
3. If you paper filed, were the copies you sent with the 1040-X in April actual copies of the signed copies that you filed in January, or just an extra printed copy?
4. If you efiled, did you send a copy of the 8879 with the copies you submitted with the 1040-X?
(Also not a tax expert, but I do volunteer for AARP Foundation Tax Aide so I know a tiny bit.)