Problem with slick flooring is that I'm sure Phyllis does what Caesar did when he was in breeding mode and would brace himself with his back half against the back of the cage and then just push and literally lift his body off the ground and shake violently while pushing.
As for the 'tube loop', that is a good idea. Could just use big plumbing size pvc piping and just build it the same way you would build a small climbing pvc jungle gym. Just use straight joints so you can break it down into manageable lengths to clean the inside and use 90 degree ones to bend it back around. Then just drill 2 holes next to each other on the either side and use big zipties to secure each section to the other.
I would use PVC piping that was thick enough for Phyllis to go through but not thick enough to double back on or else you could risk her getting stuck.
And btw, that is some serious swelling. Caesar would get some bumps and lumps from his breeding pushing but nothing that bad. Holy cow.
