Nem: Been a long time since I've used trax but I'm pretty sure grouping your object to itself and then keying this new group's translate Z should do the job.
The main problem i found with trax is sometimes mixing keyed animation with clips could lead to popping/judders... also blending between two clips often gave very unpredictable results (though that was probably lack of expericence on my part)
I did my final uni project using trax also (teaching myself as i went along like Jim [whom i sympathise with totally!]) and whilst the final result was pretty ok, I'm going to redo it all but using keyframes - using trax (for me at least) seemed to mean sacrificing alot of control.