That’s the thing, you don’t just need availability in the booking class, you need a fare that covers it as well.
So there might be a LH fare that covers LHR to PER on all the carriers and in all the booking classes you want, but from LH’s side, it would simply be a W/V/Q fare with routing rules specifying which partner booking classes are allowed. But you can’t access those using the matrix filters, only the fare(s).

I would do it like this:

- Use “alliance star-alliance” (or other ways to filter the route and airline)
- Possibly disallow codeshares (if that’s relevant for your upgrade)
- Finally filter out fares one by one that don’t fit your criteria (using the F option)

So I would simply exclude specific fares that are useless to you, until you get a good result.
I’m not an expert though, maybe there is a better way.