I installed brand new Automatic washing machine taps, recut the washer seats & what I thought was impossible, happened... it still leaked. I cut the seats again with a new seat cutter.... still leaks. The seat does not appear to be an insert so I have no other ideas. Anyone have any thoughts?
If they aren't hexed holes then they aren't replaceable, you might have to put a hex bit in to confirm removability. It sounds like you removed too much. If the seats were scratched, pitted or therefore defective, then you should've put new good ones in instead, if possible or returned the taps. But, you shouldn't touch the seats unless or until they leak & if you do it should just be a light few turn honing.
If the seats started out like most seats, being proud or raised from the shoulder, but are now flat or even with the shoulder. Then, you took way too much off. Only the seat is your seal, not the entire shoulder. You'll either need to get new seats, if they remove. Or, have to go to thicker washers. Or, get new taps with replaceable seats & not touch the included seats.
From the statement that you are cutting your own seat seals it says that you have some stock flat stock. Are you sure that the material in use is thick enough for this particular faucet?
A couple of other things to consider:
Possibly you may want to try the hardware store to see if they have ready made seals. These are often much more pliable than the flat stock you cut yourself.
Some faucets have an optimum seal that is not an ordinary flat washer style. This may require the selection of a ready made seal specific to that type of faucet.
Have you inspected the seat inside the faucet? If it has either mineral build-up or a damaged/pitted surface it may not be easy to get any seal to work correctly. In this case your best bet is often to replace the faucet.