Did you cap your substrate with sand or some small gravel at least? As long as you do that and dont dig around all the time it shouldnt be floating around your tank. Another possiblity is that you have diatoms, a type of algae. In that case you just need to get things in balance. Otocinclus love diatoms and would be small enough for a tank size. A baby bristlenose or rubberlip pleco would also do the trick.
Capped mts is one of the best budget friendly substrates you can have, and you can always buy some root tabs to replenish or assist it and supplement with column dosing to increase its longevity.
If you still decide to swap substrates and use something inert that will not leech ammonia, you can use your old filter and squeeze out your sponge in the tank or leave a little of your previous substrate behind to help with colonizing the new substrate. Ive done this many times when swapping gravel or starting a new tank. If you have plants that will help a lot and just go light on the fish food for a few days. You can even get away with not feeding them for a 3-4 days to let the bio filter catch up.
If you use aquasoil or the like you will have to wait to add fish. As for removing the mts, which I dont recommend, just tank the big part off the siphon and use just the hose by sucking on it to start it, the suction is greater and should rip it right out without any mess.