You received lots of excellent information in changing your cat's diet.
As for your piggy Sylvester who you say has "no conception of being full so he will continuously eat and drink", he should alway be fed separately
away from Mayberry in another room or in a carrier, as overeating can cause diarrhea. It is best not to free feed or leave food out. Feed them twice a day and then remove food after they have finished. If Sylvester is still not gaining weight, you could feed him an extra small meal before you go to bed.
As for picking up something from the gecko and the rat, I suppose it is possible if they are in contact and interacting with them, but I assume your vet has tested them and ruled out that possibility?
Hope you can get them straightened around soon.