Trailgators appear to be compatible with rear racks although they will restrict what can be carried on the top.
A serious amount of faffing about but you could lift the seat post to fit the trailgator attachment for towing, remove it and lower the post for your stoker when the towed bike will be ridden. The trailgator would need to be strapped to the rear rack for your journey home.
Yep - the limit isn't the rack, but the lack of seat post, and the very low height of that seat post if it was available.
The seat post is also not QR (Although it is 'only' one bolt, compared with the pair which hold the captain seat post in place.
Alternatively a bit of shedgeneering to attach a seatpost stub to the rack, remembering that you only intend to tow a riderless bike.
I had thought about that, but if I'm going to shedgineer that much, I may as well save the £50 from the gator and just do the whole lot.
If only you had an old trailer to hand, like the one you've listed in For Sale.
Again, I've thought about it - quite a lot as it happens - but I want to avoid having to tow an empty trailer around. I wonder if there is some way I can make a trailer that would sit on the rack?