Here's my recommendation.
Get VMWare Workstation. Stand up your MDSes with 77.30 and take an export of your production boxes and import them into your VMWare MDSes and test the upgrade there.
Whether you do an in place upgrade or a migrate/export/import upgrade to a fresh install, test, test and test some more.
In our case, when we went from 77.30 to 80.10 we had a large number of issues that required us to engage pro services to work through the issues. In our instance, we had a dedicated environment for 77.30 and 80.10.
Engage your SE's, use them as resources to help you get it done.
While I can appreciate your management team's fear of doing one MDS at a time (I've been known to do 1 gateway one week and another gateway the next week), I wouldn't advocate you actually doing that to your management platform.
Here's why -
If your upgraded MDS fails, and you're not taking daily backups, you're going to be in a world of hurt. I guess if you want to implement a change freeze, you could get around that until your backup is upgraded. That wouldn't fly at my rock quarry.
This is where VMWare Workstation can also come in handy. You can use it to test your upgrade path, and you can use it to test your roll-back path should something fail with the upgrade.
If you can demonstrate that you can take a fresh install of 77.30 and import the database, and bring the environment back from the brink, then there's exactly zero reason to not do the backup MDS in the same change window.
When I took us from 80.10 to 80.30, I exported the database and took the time to validate not only the export was valid, but the mds_backup was valid as well. This added about 3 and a half hours of work to my change window. But I'd set it for 7am until 11pm and still went into the next day.
If you take nothing else, test your migration thoroughly. And when you're done testing it, wipe everything out and do it again. Make sure you validate checksums of your data (md5sum in Gaia expert and Hashtab for Windows). Keep your export/backups in 3 or 4 places while you're doing the upgrade.