Good idea! You wanting suggestions for height and width? Part of width is that if you're trying to intersect bugs, I'd go wider rather than narrower myself the way a chicken moat is supposed to work.
https://www.motherearthnews.com/homesteading-and-livestock/garden-pest-control-zmaz88mjzgoe/
https://www.noble.org/news/publications/ag-news-and-views/2019/april/using-a-chicken-moat-to-grow-fruit-vegetables-and-raise-poultry/
I think of chicken "tunnels" as only for getting birds from one spot to another, rather than as an area for foraging and bug catching. If you do choose the "tunnel" approach, I'd make sure it was in small sections that can be lifted for access in case there's a problem and humans need in.
The moats in the link are large
enough for humans to enter - although the second link looks like a typical adult would have to duck somewhat, they at least wouldn't have to crawl on hand and knees while carrying an injured chicken to get it back to help! Been there, done that with poorly designed runs the former owner built.
I have some portable
shelters I made for momma ducks with ducklings that are 4ft x8ft buy a smidge over 4 ft high. They are supper easy to move, and at the moment I have a small group of
chickens living in one. I move them every day. Something like that which you moved around the
greenhouse a patch at a time might be helpful if the cost of fencing the whole area seems too much. Personally, I'd still start saving for the sort of set up the first link shows, but something portable might help in the short term.