Anything wrong with moving from a washable mesh HVAC filter to disposable

You can cut the electrostatic filters (like Filtrete) down to size without altering their effectiveness. Just buy a size that is larger and cut it down with tin snips and/or scissors. When I do it (and I have done it many times) I use painter's masking tape to "seal" the cut edge.

If you install it in the plenum of the forced-air unit, make sure you "seal" the cut edge well so the blower does not blast fibers or pieces of the filter media out into your ducting. If it installs in the return-air grill it may not be as important because the force is usually less.

Home Depot and Lowe's only carry sizes that sell well, check 3M's web site and see if they make them your size. Then go to your local mom-and-pop hardware store and ask them to order a few. Try to shop at the local shops instead of the "big box" when you can.

I'd start by trying to figure out where the dust is coming from. Do you now have carpets where you used to have hardwood or other non-fiber flooring surfaces? Especially old or broken-down carpets can be a big source of dust. Also you could have a different environment outside that has more dust in it compared to your previous location(s) that's working its way into your apartment? Possibly a different cooking environment (or no vent hood to evacuate cooking odors). If you do have a vent hood, beware that with many of the vent hoods they don't actually remove the air, they just run it through a charcoal grease filter and send it right back out into the air.

It's also possible that your old places with the high-quality HVAC filters would be similarly dusty if you hadn't had those filters in place.

Probably need to figure out where the dust is coming from, and try to mitigate that as much as possible. If that's not possible, then probably the only other solution is to buy multiple air purifier units and distribute them throughout the rooms of your apartment. If the noise is objectionable while you're in your apartment, you could put them on timers to run only when you're not there.