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surprised the workshop hasn't got a core remover; this will allow a much higher instantaneous volume of air into the tyre, and hopefully input rate will be greater than leakage rate, et voila!
lighter fluid is another trick, or butane gas.... if you try these please post pictures of your singed facial hair..
car tyre places initially blow the beads into the rim seat with the core removed, then plunge the core in and fine tune the pressure
Sadly the compressor pictured does not have a fitting that works with bicycle valves, and the other compressor which does was feeling a little sad and needed some alone time.
Hopefully it will recover it's equanimity soon.