2nd, I have never heard of peck tapping
Many controls can rigid peck tap. Fanuc, Mazatrol, Haas, etc. I'm pretty sure that a Mitsubishi control can as well (being that they build the Mazak controls). You don't need a compression holder for this. Heck,... you shouldn't even need it for what you're doing. You should be able to do multiple depths in synch mode like this:
M29 S???
G84 X0 Y0 Z-.5 R.2 F??? (First depth)
Z-.75 (Second Depth)
G80
Most machines can do this all day long. You can even tap a bunch of holes, return to home, and run the tap cycle again and still pick up the lead. As long as you don't adjust the tool length, work offset, R plane, or change taps, you can just simply restart your tap cycle. You can even change the Z depth of the cycle and still come out fine if you're adjusting a set up.
Now, for peck tapping. JDSmith, you're code looks fine for most controllers. The "Q" will force the peck. For many machines, there are a couple of parameters that will control this. You may have another parameter that needs to be turned on to allow peck tapping. Or, be sure of the allowable value inputs for the retract parameter. Many machines will also have a parameter for the type of peck. You may have the option of full retract (similar to G83), deep hole cycle (similar to G73), or even a setting for "none". Look for this parameter as well. You're retract value is awfully big but if that's what you're looking for.....
One question, does your machine at least "appear" to be going through the motions? Also, noticed your "X0Y0" and G80 is using the letter "O" instead of a zero. Typo?
It's just a part..... cutter still goes round and round....