FOLKS, I have a solution. It took me ages to come up with this. However, you do have to live with the patch residue for a day. It's very cheap though.
When you take the patches off, get a small blob of some kind of emollient cream - i use Aveeno cream for very dry skin - and wipe it over the residue. Don't even try to get the residue off, just wipe it on and leave it.
Next morning in the shower, get some shower gel and your sponge and it will just rub right off really easily.
Ta da. Zero other products. Zero expense. But you do have 1 day with residue.