Perhaps I can offer a couple suggestion here that might work for you. First one is money, the second is labor-intensive, but both work well and might sway Mr. Bill in favor.
😀
We have a trampoline that we used for wrestling training, to help the guys get comfortable learning and perfecting aerial maneuvers before taking it to the ring. In order to keep them safe, we spent the extra money and got the screened enclosure. It kept several men, one at 250+ lbs, from sailing off the trampoline on more than one occasion, so I can testify that they work extremely well in keeping little ones on the tramp.
Secondly (and this is something we actually plan to do when Jordan is older for his safety, although ours is a 15' round, so we've got quite a task in front of us when we finally decide to follow through): If the concern is not only the possibility of jumping off the trampoline but how high it is off the ground, it's possible to put the mat and frame directly on the ground by digging a hole underneath it. Using one of the smaller tramps makes it less of a PITA, and if you don't mind the grunt-work, it also works well, plus doesn't make the yard look so "crowded".
And I have to say...I learned, and Glam can also testify, that "drunk-jumping" can be incredibly fun when you got a trampoline in your backyard. Once again, the screened enclosure is a Godsend.
😉 LOL
~ Mistress Aura