I JUST went through this last year and what worked for me was negotiating with local(ish) buyers through Facebook Marketplace. I sold my entire NES collection this way and the buyer got an awesome deal and I saved a ton of time. Could I have gotten more out of it through eBay? Probably, but listing and shipping, and dealing with buyers...forget it.
The things I did sell on eBay: boxed games, shipped in boxes. All of my Genesis games--most were in plastic cases with UPC codes on them, so I could just scan it with my cellphone to add to eBay. Also easy to ship. A couple of logical game lots, the largest using Atari binders and a few other cool storage folders etc. All the Intellivision cartridges in one lot, flat-rate box. A really nice Atari computer lot. Joystick lots, also flat rate box.
Psychologically speaking, the purge has done wonders. I went from a full-on gameroom to a closet in our office and don't miss the cartridges at all. I kept all my multicarts, etc. Found a way nicer CRT TV than I'd had, all my favorite consoles are still plugged in, and I'm honestly playing a ton of old stuff on the Nintendo Switch now!
Good luck with your sale. It's so hard--drove me crazy for months and I had the same instinct you did--if you look at my posting history you can see how many times I was just hoping someone local would come take it all away.