So the wires on my O2's are cut right at the sensor. What kind of problems would I expect to see in this situation?

 

Starting with the obvious "CEL" will be on, it could have misfires, backfires, power will be affected, it will probably run rich as with no information from the O2 sensor your Disco don't know how to adjust fuel amount - since it can't tell the current state (Rich Vs lean etc...) MPG will be even worse than usual.

Long term impacts are very bad for the health of your engine - assuming you do not care about poor emissions.
My suggestion would be to contact Paul Grant ASAFP and get a replacement or source one locally. They are not hard to replace - well comparatively.