Good to increase the temperature slowly so the fish can adapt. Cool water species probably cannot handle it high enough to kill Ich, though (86*F). You can highly likely get it into the mid 70s, maybe a bit higher. This will increase the metabolism of both Ich and fish. Fish can fight it off better, and Ich will grow faster, fall off the fish faster and become susceptible to treatment faster.
Increase the aeration in the tank when you are raising the temperature. Warmer water holds less oxygen. Fish gills may be compromised by Ich in the gills.
I do not think the sponge filter will remove them. I think it will give the adult Ich more places to land on to breed.
Add ultra violet sterilizer to kill the free swimming Ich.
I understand about not giving the substrate a deep vacuum. That is not necessary. The intent is to remove the Ich that land on the substrate and most other surfaces in the tank. They do not burrow into the substrate, though they could fall in between the pieces of a gravel substrate. In a planted substrate (dirt, plant media, other fine materials) the Ich just sit on the top.