If the $1000 limit is a hard stop I would keep using what you are using or get a cheap pump for the interim and keep saving. O/u’s are more complicated to make, and the benefits that come with a double gun (to me that is mostly faster handling compared to nearly all pump or autos) are lost in 100% of the cheaper ones I’ve seen. In my opinion a double gun less than a Beretta, Browning or one of the other Italian makers is not worth spending on at all. Keep in mind this is not to say that they don’t work for low-round count shooting, I just don’t see the benefit over a pump or auto at that point. At that price point the pump or auto is going to be a better quality gun with better long-term service and better resale value, and it will last longer and perform better over time. I don’t remember all of the names, but there are some house-branded Italian made shotguns that were sold under various brands for relatively short money. A lot of these were made by rizzini and some other brands before those brands had their own distribution in the US. Those guns are the best of the inexpensive over and unders that I’ve seen, by far. They’ll be marked as made in italy, gardone v.t. Or Brescia, and they’ll have the characteristic low-profile reciever and lines of the less-$ rizzini guns (There are multiple brands called rizzini, I’m not certain but I think i.rizzini is the one I’m referring to, sometimes called f.a.i.r.). Fausti is another italian maker that has had some decent inexpensive guns. These are basically guild guns, there are gun factories in that area and various brands contract to have guns made by the same factories. They are essentially the same design and parts on all of them, just with different grades of steel and different finish work applied, etc. A older winchester 101 with fixed chokes or a miroku (same gun) can also sometimes be found in that price range and would be a good option. An older beretta BL3 or bl4 could also be a good option, the 20-gauages ar epretty exceptional handling and get a higher $, but a 12ga is a decent, basic O/U that will handle and last better than any of the modern sub-$1000 new O/U's.
Of the brands mentioned in the original Post and since, my preference would be a CZ simply because it’s a bigger, more reputable company with more shotguns out there and shotguns make up a big% of their business, so I think you are more likely to get service or parts if anything goes south over time. But you DONT get the weight and handling characteristics that to me are really the reason why I like double guns.
At that price point You could do a lot worse than look for a good shape Winchester model 12 in a lightweight configuration, or a newer Beretta or benelli auto. You can get a lot of gun for well under 1000 bucks in one of those.