Any positive displacement pump is variable output by changing the RPM The electrically commutated PMDC motors are fairly efficient over a broad speed range. So there is no need to use a variable displacement compressor with a variable speed motor. A little Sanden with a direct drive (no belt losses)...

Use a similar sized valve - forgot about the external equalization. Unless you live in some remote spot, there is an industrial hose shop somewhere nearby. The Aeroquip stuff works well, but you need to use the whole system - hose, fittings & tool Some odd MVAC fittings are not available from Ae...

If you had both service valves closed during testing, then yes the high side is too low for a good compressor.

Given that you have a POA valve, this is probably an A6 compressor?

Year / Make / Model would be a big help in helping you diagnose this system

I believe the 1979 Mark V still had a POA valve on the low side. The low side should remain steady, and around 30 psi. That heater valve was a great idea 40 years ago. They are subject to the ravages of age, and poorly maintained cooling systems. Since it is 105f here in Las Vegas right now I would ...

Use the TXV for the 1972 GM line - C20 / Suburban / Impala etc all used the same valve. Go ahead and use the accumulator along with a Receiver in the liquid line. I do this on TXV conversions, you get a second dryer. Add 1.5 to 2.0 ounces of oil for the added dessicant & the puddle in the bottom...

Check the compressor clutch gap.

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No RPM readings in the video, so it is hard to determine what is going on there. The regulating valve never moves and a pressure sensor shows what may be the high side going all over the place. Without actual system pressure from both the low & high side & an RPM reference it is all guesswor...

Rapid cycling, at HIGH HEAT LOADS is absolutely a problem. In systems controlled with pressure switches, rapid cycling at high heat loads is either a significant undercharge or cycling on the high pressure cutout switch. Almost always associated with CCOT systems. Your cycling occurs at minimum heat...

Same compressor, same clutch - either TXV or CCOT. I used the CCOT as a common example of a system that will cycle the clutch for it's entire life.

You seem to be obsessed with the cycling. It has probably done this since new. If it bothers you, turn on the rear system.

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Rapid cycling can happen with any CCOT system in the right climate conditions. It does not hurt anything, and the compressor / clutch is designed for cycling. The solenoid valve in your system shunts all of the refrigerant flow to the front TXV when closed. I would expect cycling on front operation ...