Sorry I should have mentioned anything over 6 feet *should* be okay if they flush

so they *should* be falling back down before reaching six feet so a walk in run would work
An idea would be to have the foot high run hinged lids with an "underlid" of bird netting that is marketed to keep birds off of your fruit trees. You could cut several inch slits in the netting so it appears as a barrier to the birds but even if they try and fly out (they honestly don't really think they're in captivity so there's no "escape urge" hehe) they will be blocked by it.
Then you can use those slits as access within the run to pick up eggs.
You can encourage the hens to lay eggs in one spot by putting hay there (possibly contained in a little open top low wall box) with several inch tall grass, even potted would be appealing to them. This isn't a promise but that is what they crave and they may end up all laying there. I would say chances are pretty good they'll all gravitate there.
For clean outs you could easily train the quail to go into their shelter box at the end by putting a big sand box in there and tossing in a handful of finch seed or other treats you can keep on hand out there. Make the treat noise and they will come RUNNING xD
For my coturnix quail, before I give them treats and when they first get to them I make a kissy sound. After only a few times that kissy sound makes them suddenly hyper alert and trying to get at me holding the treats through the cage - the only time they ever try and jump out haha!
You could use whatever sound you want but a unique click or kissy sound would be better than a word.
So you go to the shelter box, toss some seeds in the sand (or wood shavings would work) and make the kissy sound before and during their enjoyment. If you have a good male he will make a tidbitting sound like a little "woop woop woop woop" to get his girls to go to the treats "he is providing" so that's kinda what you're doing
Once they race into the shelter box you could slide down a barrier so you can work on the run or pick up eggs. Honestly they'll very likely be focused on the treats for a few minutes and then drink/rest after the frenzy
I love my walk in aviary but it's only 6x6 feet with logs and plants in it so I have to be very careful where I step so I don't crush an egg (there's tall grass all around so they sometimes make random crappy nests hehe) or step on a quail or their poop

most importantly I don't want to hurt the quail because they camouflage so well, have to be careful every step since mine is so small.