I can't seem to get any sounds from mine. Using an iPad Mini, Jamup Plug and Jamup of course. All I can hear through my headphones/monitors are noises that the mic picks up and if delay is turned on for example, it will affect that noise. Sounds coming from the Jam tab as well as the metronome...
There ya go.
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Most of their SE's...
Since you're in the UK, have you considered the Chapman Guitars ML-2?
I'm not too sure about the pickups, but the guitar seems to match most of your criterias.