I am not familiar with the 5Z3, but tubedata.org is your friend. Look for maximum current, Vdrop at current draw, pinout, etc. If your power supply is cap input and it has a big cap that the GZ37 can handle but the 5Z3 cannot, you might have problems. Maybe if I have some time later I'll look it up and get back to you.
The choke Q: inductance (mH) isn't a constant, it is rated for stated inductance at a particular current. So your choke might be 10mH @150mA but 1H at 10mA. Also, one needs to mind the voltage (insulation) ratings. If you overdrive a choke (too much current) you will saturate the core and that results in a number of bad things like, but not limited to, poor bass response, humming, really bad sound. Best thing to do is ask Jack @ electra-print.