First, test your outdoor speakers by connecting them to your main channels to determine if they are functioning properly; if you bring them inside to your listening room with short interconnects and they still require you to crank the volume, there's your problem.
Next, test the zone two output of your receiver. Try your zone two output using short speaker wires in the same room as the receiver is located; this would narrow down the problem (i.e. is the problem in the wiring or the receiver; is your cable run to the outdoor location too long for the guage of wire chosen...although I would expect this to roll off the highs rather than damp the whole signal). You can test your zone two output with any speakers you know function properly.
Long wires and high impedance speakers would yeild low output, requiring you to crank the volume, but I wouldn't think that would cause shutdown circuitry to kick in-thats usually from trying to push too low impedance for the receiver. Higher than normal impedance and/or lower than average sensitivity speakers, being driven by a lower output zone 2 through 200' of 20g wire would definitely be muted.
If you determine that the speakers are fine and your zone 2 output from your receiver is adequate, next go over all connections again and make sure you don't have a stray strand of wire causing a short somewhere, as that could definitely cause your receiver to shut down. Be sure to check all possible spots where this could occur, at the receiver, speakers, and anywhere in between.
The source bleed-through sounds like bad switching relays in the receiver. This may be just the way that receiver functions, and if it is not perceptible at normal settings of the volume, figuring out why the zone two requires such high settings and reducing them will alleviate the problem. Hopefully the bleed through problem is this easy to solve.
Not sure if you've already tried any of this, hope it helps narrow down the problems.
