As you have discovered, almost all theatrical LED fixtures use constant power and either DMX or some flavor of ArtNet to control intensity and other parameters.
There are a couple ways you could go.
1. I've never seen the fixture you bought, but I'm confident it has a manual mode. You're not the first one to have to run it without a controller. It might be worth a test to put it into manual mode, bring it up to the desired intensity (full) and then cut the power and then power it up again. If it works you can replace your dimmers with switches and put up with not having a nice smooth fade up and down.
2. I've never actually seen one of these in person, but this fixture has an option to dim on mains power. It will probably be much more expensive, but I expect it would perform better in almost every way. It's made for theatrical dimmers using some flavor of phase control to reduce voltage and I don't know how different that is from household dimmers. But it might work!
3. If it were me, and I was happy with the output of that fixture (hmmmm😀), I'd just swap the dimmers for switches or wire them to be always hot and get a cheap dmx controller and some DMX cable. There are also inexpensive USB interfaces you can use with free or very inexpensive software, but that just adds complexity. It seems like you need this to have a very simple user interface. 4 sliders is pretty simple. Again, I've never seen these fixtures, but I wouldn't count on them having a super long life. So using something very standard and very replaceable may come in handy. 🙂