Sorry to hear you guys received such non-standard non-rules TPS events. I ran and designed the Maine TPS event this year again. Groups rotated among three stations:
Station I: Isolating and identifying the fundamental frequency of a vibrating rubber band, using a Vernier microphone sensor connected to the TI InspireCX handheld. (Hence, a station on Harmonics.) I'd expect a National tournament might have sonometers (stretched music wire, similar to a "flat" guitar). You could try out probes on a guitar, and see if you can identify the harmonics.
Station II: A closed cylinder of unknown volume had a Vernier pressure sensor connected to a TI InspireCX handheld via one port. A second port was attached a graduated syringe. By compressing the syringe a known volume, find the pressure as the volume is increased. As a result, work backwards to estimate the unknown volume. (Hence, a station on Pressure. Since PV = nRT, assume T is reasonably constant, nR is very constant, thus V is a function of (1/P). When you get to half atmospheric pressure, you know you've doubled the volume. Read the volume off the syringe, and you know your unknown volume.) PV = nRT. It's not just the law, it's a good idea to really understand this equation, as it explains about everything. Throw in knowing density D = m/V, and you know why hot air balloons rise, and cold air balloons, even cold helium-filled (put balloon in liquid nitrogen) fall.
Station III: Known quantities of sugar, yeast, and water at 70 degrees C, are added together. A Vernier temperature probe on a TI InspireCX handheld gives you constant readout of temperature digitally and as a graph. Determine if there is a temperature increase or not with the specific amounts of substances. (Hence a yeast catylase reaction, using a Temperature probe.)
Tiebreaker question: The classic TPS question: Estimate how many Whopper candies of a known size given will fit in a cylinder of known size given.
It wasn't perfect, but it was in the spirit of the rules, and I think comparable to what one should expect at a National Tournament. I can only say, that I feel badly for those of you who didn't have a rules-based experience like our teams in Maine had. As the event sponsor, I can tell you it took only a reasonable amount of planning. Texas Instruments loaned all of the equipment we needed for probeware and TI handhelds (I'd expect you'd see exactly the same at Nationals), and I only had to gather a few other pieces of apparatus I already have in my physics department.
Best of luck to you all!