Try putting the anode in a tightly-woven cloth bag and submerging that in the electrolyte. Depending on what electrolyte you use, you'll need to choose an appropriate material for the bag that won't break down.
The bag will keep all the slimes inside. Sreetips on Youtube does this with his silver electrolysis, but to keep the waste slimes OUT of his pure silver crystal. It does an excellent job of keeping all the ultra-fine slime out of the electrolyte, so it would certainly work for saving the valuable slimes as well.
Something like a nylon filter bag might work for most electrolytes as long as they're not too acidic. Nylon, since it's an organic material, can then be ashed, and the slimes will be a dry powder mixed in with the ash. Nylon itself, being entirely carbon-based, should leave very little ash when totally incinerated. Most of the powder you're left with will be the PM slimes.