Yeah, if you are on a newer latest dev build, you may try installing Disposable Theme v3 directly. At least you will have something working in your hands, of course it will not reflect your va colors or logo images etc but we will be sure that the core theme files are intact and ok. Then you can slowly work on it, by following duplicating procedure (explained in the readme and here at the forum), you can have your own copy of DT v3, edit only the pages you need, have your own stylesheet for coloring etc.
All this may be hard on a live server while your pilots are flying on it, but at least it will be better than having lots of errors around.
Hope you figure this out, maybe you can send an email to all your pilots or a discord notification to stop flights for one/two hours while you are doing the update, installation of new theme and module pack etc. At least your logs will be clear, server will not be dealing with getting pirep updates / accepting them etc. Or you need to find a good time, maybe when all your pilots are sleeping You will be awake and working on the update.
It is still not good to do all these on a live server but looks like you have no choice at the moment.
If I were in your situation I would probably;
1. Stop all flights
2. Switch to default theme
3. Make a database backup
4. Clean cache manually (explained in docs, update section)
5. Update to latest dev build
6. Test if it is ok (with default theme, check every single page it offers)
7. Install Disposable Theme v3 (latest release)
8. Switch to it, check if it is working ok too
9. Have a duplicated theme based on DT v3 (explained in readme and here at forum)
10. Switch to it, check if it is ok too (no edits at this stage)
11. Install Disposable Basic Module v3 (latest release) and test
12. If all is ok, let pilots fly again, slowly work on the duplicated theme to have your va colors, background image etc back, one step at a time.