Like you, I tend to scratch with the uncapping fork, but I always seive the honey as it goes into the bucket (to recover the cappings).
So do I, but not simultaneously with extraction as I find the usual two stage sieves tend to get clogged with wax (made worse by my uncapping method but compared to a huge bucket of honey and wax sliced off by an uncapping knife its infinitely preferable)
I've recently acquired a very tall settling tank with a pair of much coarser two stage stainless filters that should be better in this regard, but I'd need to locate the extractor right up in the air to be able to dump it straight to the tank...or build a pump
Hence my current solution, a honey bucket with a tap, the extractor gets emptied in one operation and moved out of the room, nothing is unattended as the honey flows fast enough that you aren't tempted to wander off to do something else in the meantime.
Honey then gets filtered using a two stage (nylon) sieve in another separate operation. If I leave the honey for a few hours the majority of the wax is at the top of the bucket and with the tap being at the bottom the honey goes through the filters quickly and the filters don't get clogged.
I've made a stand to hold the rectangular tanks at a suitable angle so that they drain almost completely. It's
nearly impossible to have a bucket overflowing because one bucket is the same size as the next.
All my cappings I will dump in an ashforth feeder with the separators removed giving the bees full access to clean off any honey, suitably cleaned they will be washed and then melted into blocks.