Whatever solution you undertake, you will need to check your setup, particularly the parallelism of the blade and miter slots. Even on a new saw, this is a critical step with any saw. If the table isn't really flat, you'll find it almost impossible to get good cuts, but flat is pretty relative. If you're using feeler gauges, most manufacturers consider 15 thousandths to be flat. If it is much more than that, you'll have problems. Theoretically you could take it to a mahine shop and have it flattened, but you might be better off just biting the bullet for a nice hybrid saw. Even then, how you set the saw up will determine how well will do what you want.
Most stock miter gauges are not very accurate if you rely on the protractor settings. But with a really good engineer's square or a draftsman's triangle, you can adjust the angle to exactly 90 to the body of the blade. Not the cutting tips, the flat part of the blade. You can add a very straight board to most miter gauges, and apply a self adhesive strip of sandpaper to the front surface of the board so you don't get slippage. I have the thick triangle from Rockler. Very accurate.
I make a lot of picture frames, and had a devil of a time getting perfect mitered corners. Finally turned out to be the narrow kerf blade. I changed to a Freud glue line full kerf blade and the cuts became flatter. The narrow kerf blade deflected slightly mid cut. The full kerf blade cured all that.
Do immediately buy a Wixey angle gauge. This lets you set the blade angle precisely to 90 to the table. A slight error on that angle will mess up your assembly. Cost is $30 on amazon. If you get a news saw, you'll use it. Use it every time you move the blade. Crank the blade all the way up to use it.
I had a decent Delta contractor saw for several years and it worked OK, but then I got a Laguna Hybrid and it is a brand new world of accuracy and performance. But even it required a careful tune up.