Just to chime i a little here (I find this thread fascinating...and don't take this the wrong way, the probs encountered are to be embraced/welcomed as we all learn from the quest to solve).....
ok, just wanted to float a concept here - IMHO, this 'tremolo' is actually more akin to a kill switch vs a traditional tremolo.
(warning: oversimplification for the sake of putting a point across ensues!)
kill switch - swings between inifinte resistance & a dead short....the load as seen by the source changes (a lot!) - current is the affected one here.
traditional tremolo - swings between full voltage and no voltage - or variations within those limits (think 'potentiometer' moving up and down quickly - the wiper being the output), the load as seen by the signal source stays the same - voltage is the affected one here.
the ldr in the tiny tremolo is acting like a polite kill switch...it's not infinite, nor is it short....but bounces back and forth somewhere in between these boundaries. There'll always be some source signal loading (albeit not too much impact at the dark end of thing, *if* a high dark resistance ldr is used), equally the signal will never fully get down to nothing...close but not fully killed (IMHO it's a bit of an aural illusion.... a similar analogy being an optical illusion to do with your TV ....when it is switched off the screen is actually only dark grey...but when you turn it on, there and watch something you'll swear there 'appear' to be deep, deep blacks in there!)
Anyway, I'm rambling....I'll get me coat!