First post so forgive all the questions.
I have been running the common form of #37 for over a year now with very good results. Typically, I will run it consecutively, adding 5-10 pounds per month to each lift. With this new three month program outline, I'm unsure of how to progress. Should poundage be added between cycles, or only at the end? Additionally, what if I don't plan on maxing as often as would be called for in the 3 month plan? Can I just bounce between #37 and #31 for as long as I want?
You seem to be using #37 like it is 5/3/1 or a similar undulating linear periodisation template. The way you've been doing it is not really how the program was intended to work within a longer training plan. #37 is just a 4 week preparatory block to be used as part of a larger periodised program.
The progress comes through skill development and by stressing the lifter through the preparatory period (#29, #30, #31 and #37 are all examples of prep cycles) by undulating training volume, then allowing the lifter to peak using a comp/peaking cycle (eg #32). You use the same 1RM throughout the entire 3 month program.
Progress doesn't come from increasing poundage in a linear fashion, ie fixed increments every 4 weeks. Although that has clearly worked for you in the past, it is not sustainable.
If you manage to increase your 1RM in the skills test in the first week of #32 or at the competition/test at the end of #32, you use that 1RM the next time you run the cycle.
It has been suggested that if you find the prep cycle too easy, you are better off increasing volume (more sets, more training days) rather than adding poundage, as this will allow better skill development and reduce the risk of injury.