Can you take another look at acrylic glass? I find it at least more high-quality in appearance than plexiglass or polycarbonate. I think it should be possible to glue it...
I gather that you have a small budget. So do it right the first time and let the glazier handle it, otherwise you'll pay twice. Even though I do not at all believe that 1,000 EUR is not a lot of money... here it is well invested. If you fiddle around with plexiglass yourself, you'll want glass anyway in a few years. You get what you pay for. Unfortunately, that's how it is.
Can you check again for acrylic glass. I find that at least more high-quality in appearance than plexiglass or polycarbonate. I think it should be possible to glue it...
Plexiglass is acrylic glass. Plexiglass is just the brand name. If the budget is currently too tight for a glass solution, then I would make do with a shower curtain for the time being until the budget is sufficient for glass.