"Won't touch a motorcycle" ... no, you don't want them too either ... however they might change the tyres .. if YOU remove the wheels and have the new tyres to mount. If they are strict they may not let you 'work' on your motorcycle on their property .. legal insurance reasons.. but you can do it on the side of the road.
The other alternative is to use tyre irons on your rims .. and you may mark them. Depends on your tyre irons, skills and practice, the stiffness of the tyres.
Other than that .. your stuck. Or your bike is. You could leave the bike behind .. and bus/hire car back .. then return and pick up the bike later. Depends on how much you "need to get back". $$$
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