Found the Country Gent info, such as it is: Jonathan Richman in Uptight p86
"Sterling helped Lou work on the Country Gentleman by giving him a pickup off his own Stratocaster to put on it. That's brotherhood. .... the Country Gentleman had four pickups (they usually have 2), built in pre-amp, built in tremolo unit, added Gretsch pickup, added Stratocaster Fender pickup for more treble. ... the Gretsch was converted to stereo enabling him to get low bass and high treble at the same time."
The reference to it being stolen I can't find. Probably just a passing comment somewhere. Anyone else remember it?
The plug in distortion thing? I had thought it was built into the guitar, but it seems not - it was probably one of these:

and another pic showing the switch:

You can definitely hear something being switched on in a feedback screech before one of the solos in IHHCMN...