I am new to chickens, so don't take my word as gospel but I have gotten all my girls laying in nest boxes (knockonwood) and I'm glad to offer feedback based on your video.
First thing I'd say is DON'T take off the roof- you mention just leaving the poop board for coverage and I don't think that would help because hens like a cozy, private box. if you're in the mood for a rebuild, I'd actually suggest framing out the open side (where they walk in) so that it's more private and they can toss bedding with abandon. That roof piece could be hinged for easy egg collecting. I'd also equip one box with the hay/straw like you have and the other with shavings. My hens have various preferences of what kind of bedding ratio they like and they will tweak a nest to their liking.
I see you have fake eggs in each box- are they golf balls? Fake eggs may have contributed to getting all my girls laying in the right spots- I bought some plain wooded egg shapes at a craft store for less than a dollar a piece and painted them myself. Beyond that, I'd move each real egg into a nest box when I found it elsewhere and I'd keep it there until I collected the total at the end of the day. As new girls got ready to lay and they were checking out potential spots, I think it piqued their interest to see how many eggs were in each box. I have roosters and one of the jobs they do is get in the nest box (or other suitable spot to lay an egg, by their calculations) and kick around, all while talking to the hens about how great it is. If you want to emulate that, I don't think it'd hurt. When I clean the nest boxes or pat down the bedding during egg checks, I do my best rendition of that pep talk.
I noticed the hay was shaped into nests, are you doing that or are they? If you are doing it, I think you should muss it up and see if the girls are inspired to make their own nest. Even if a hen is the third one to lay in the same spot that day, my girls love to push the chips around and kick and fluff. I think it helps with the hormone wash needed to lay an egg.