Addressing the first recording: -

Assuming the MP3 accurately reproduces the analogue sound then I think the guitar may have been a bit close to the clipping point on the mixer. The more I turn it up the more I can hear a roughness in the high-mid that probably was NOT audible over the speakers because the speakers will have been smoothing it off.

Next time take extra long guitar leads and take it in turns to go out in front of the speakers (or even both go at once) to see what the speaker sound is like.

It does however sound very like what I expect a magnetic slot-in pickup to sound like.