Anyone know if there's a signal I can pick up from the hotwire system to
know when it's doing over-run fuel cut-off, or is it all done internally on
the hotwire?

I have in mind to crosslink to the LPG.  

I could adapt the rev-sensitive relay from a k-jet, but that requires adding
a throttle-closed switch to the engine and would be more hassle.

Also, the LPG is closed loop.  will it get confused, if the fuel gets cut
off?

I imagine that it will think that it's gone terminally lean, and try to
richen the mixture, to whatever extent it's able to.  This of course will
mean that it goes rich when the fuel comes back in and thus will probably
negate any saving made by cutting off the fuel in the first place...