Surely a 'hands-on' captain with initiative could suggest to the local handling agent the above ideas. Equally, assuming the final solution was organised via Ops at home base, they would also have the gumption to consider their other UK & EU bases. However, if they only had 1 tow bar each might the same problem then arise else-where? A bit like solitaire, you just move the hole.
What are the limitations on crab-claw towbarless tugs? I'd always had the idea they were very flexible. Surely EDI have those.
There was a case in 90's during a strike in FCO that, allegedly, a BA 767 was pushed back manually on the gear wheels & struts. I heard it was easier than expected. If true, they got out of there when others sat on their hands.