Travel Update:
Luton Airport was a breeze, both for departures and arrivals. Expect 5-10 minutes to shuttle between train & airport, but that was only 2 Pounds 30, and they run consistently. I took the train starting from Covent Garden Underground on my way to LTN. I later took the train to and from St. Albans (a return ticket included airport shuttle rides) on my layover. It was all straightforward, easy, and (relatively) on time.
WizzAir did not check bag sizes on any of my flights, although I'd gotten a smaller burner bag just in case, and most people seemed to have overhead bin carryons larger than the roller bag I'd normally use for any other air travel. For the record, neither Norwegian nor WOW physically checked bag sizes/weights, either; I have heard that RyanAir is much more strict with this (and they also have very particular bag size allowances).
Departing Luton Airport (on a Sunday afternoon), I walked in, went directly to an unmanned security document scan (just set my phone down for the QR code to be read and walked through), and proceeded to the security x-ray scan line. From arriving at the airport by shuttle to arriving at my departure gate... <15 minutes ...and, oddly, not one human checked my ID or boarding pass until I was boarding.
Arriving at Luton from Budapest did require a trip through passport control, but even this only took me about 10 minutes from deplaning to bathroom through customs to the external ground transportation (if I'd had an EE/EU passport, however, I'm guessing it would've taken at least 15-30 minutes just for the passport control line). In this case, a two hour layover would have been more than enough time to transfer planes (on a Wednesday morning; I was told it is usually pretty quick), but I left the airport for breakfast & exploring in St. Albans and later departed from LTN (on a Wednesday afternoon) just as easily/quickly as I had on the previous Sunday (~15 minutes from arriving at the airport; very little human interaction or security concern).
I did not have to go to the WizzAir counter at any point; just directly through security to the gate. I also did not have to check a bag, so I don't know how smoothly baggage claim might run at Luton.