You have a BiFri Tikit? or what? You dont say. Tikit will roll on it's front wheel when folded.
the bar mast fits in a clip on the frame tube to hold it straight. (Pack-it Under development Wont)

I bought a Carry Freedom City Trailer , A folded up Brompton can Lay across the top of their bag
That is slung across the trailer frame.



Once the bag is removed the wheels swing inward and the trailer folds flat.


I suppose where you go you dare not leave your Bike Outside..

your Travoy will be full of Bike while in the shop , Right? .

I suppose the stuff is in the shopping cart and at the grocery check out you un pack the bike and pack up the stuff you Bought..

I have a Pack to Travel Bike Friday Pocket Llama I wont try to fold it up much at all .
its more a Go in the suitcase at beginning and end of trip, Rig.

The fold of the Tikit (and the new Packit) are better at that.. 349 wheel like Brompton.