I actually found myself in that same situation but about 6 years ago ;-)
Although you could try to repair the database and attempt to restore it in a clean environment (that matches the old one at some crucial levels), it is very labor intensive with quite a bit of trial and error involved. The chances of success are also not guaranteed so you could just be wasting a lot of time.
I ended up purchasing a 3rd party recovery tool to export the mailboxes to pst-files which I then recovered to a new Exchange environment (in this case Exchange Online). Although these tools don't come cheap, for this case it actually was cheaper than putting in the work and the high risk of failing still. There also wasn't any real hardware around to construct a recovery environment either.
FWIW: I ended up using Kernel for Exchange Server but there are also other tools such as Stellar Repair for Exchange. If you do go the 3rd party route, make sure you first try it out with the trial software first to make sure the tool is suited for your type of data corruption.