Sigh. I wish the world would be more accepting of natural body variations. I used to get in trouble in school because I would have to leave class to go poop three times every morning. Finally I just started going to the nurse for an hour because I could poop, lay down for fifteen minutes, and then go poop again. When I got into junior high and started switching classes every fifty minutes, I just got used to being in extreme discomfort and holding it in until I could get to the next class, where the teacher didn't know I had just used the bathroom 25 minutes ago. At home, my mom was always knocking on the bathroom door and checking on me "to make sure I was OK" - as if the only reason why it should be taking me more than three minutes is illness. When I grew up and visited homes that had reading material in the bathrooms, it was revolutionary for me - wait, you mean I'm not a freak? It's normal for pooping to take awhile?
That said, I do understand the logistical difficulties. My oldest (almost 7) also takes 20 minutes to poop. Sometimes he is just sitting there for five or ten minutes, and it looks like he's screwing around, but then: he's right, there was more poop on its way. Before he started kindergarten, I also asked him what he was going to do when he had to poop at school and it could not take so long. Honestly, I'm not sure what he does, but I haven't received any complaints from his teachers, so I think he really just worked it out for himself.
Honestly, I think you have made reasonable and useful proposals to the daycare. Your daughter is 5, she does not need full-time supervision in the bathroom. Is there some other reason why she can't just go by herself whenever she needs to use the bathroom (telling a teacher, of course) and then the teacher can come check on her after ten minutes or so - not to stay through to the bitter end, but just to pop a head in and make sure she's doing OK, then go back to the classroom? I get that the teacher can't sit there with her for 20 minutes - perhaps explicitly letting them know that you do not expect her to be monitored for the entire bathroom process will help them out.
Good luck - and good for you for being supportive of your daughter and her healthy bowel habits!