I've seen a lot of arguing about cycle stops. They have thier use, but it is dependant on the needs of the user. Sprinkler systems that run a long time and need constant pressure, sure that's a great example. A house with a lot of people and a small tank, maybe another one. For myself, I have an 80 gallon tank, to go a.ong with my geo heat pump. When it runs, it will run for an average of 10 minutes, and my well pump will run once. Maybe twice, depending on where the pressure is when the hp started or if other things (like the washer, or the wife doing other stuff) is happening. Yesterday my hp ran 35 times, my well ran 40. And yesterday was an odd day as my wife had the oven on for several hours which helped heat up the house. But a cycle stop would have eliminated maybe 4 or 5 starts. So in my case I do not see that it would help. Now I originally had a small 30 gallon tank and it cycled a lot. I'm not sure if cycle stops existed then, but it could have been an option. But putting in the big tank solve my cycle problem. It all depends on the user setup and need. But that's just an opinion. I'm certainly no expert, just a user that knows his own system. But always learning and looking for better solutions. And this forum is great for that.
Since the OP was scared off, I will reply to you first as you are at least a homeowner here looking to learn something. I think that is great. But you need to be careful making assumptions about your own system and taking advice from people on forums, as some are very forthcoming with misinformation.
Your first problem is the HP is cycling. Every time the heat pump cycles the well pump also cycles, even though you have an 80 gallon size pressure tank. There is no Cycle Stop Valve that works on heat pumps, so oversizing them causes the heat pump to cycle.
My heat pump cycles about 6 times per day, and stays on for hours in the afternoon when it is really hot. The HVAC tech wanted to oversize it. I wouldn’t let him. If I let it get really hot inside, it takes hours to cool the house down. But the heat pump is perfectly sized to keep the house warm or cool without many cycles. Consequently, I have a tiny well pump that also runs for hours. A larger heat pump would cycle a lot, making the well pump cycle a lot. It would also require a larger well pump that uses more energy, and the larger heat pump would use more energy.
But yours is fairly typical of an open loop heat pump setup. Adding a Cycle Stop Valve to the large tank you have now would make sure the well pump only cycles once during each heat pump cycle. Like you say, this might save you only 4-5 cycles per day. The heat pump keeps you from seeing the cycles on the well pump that would happen from just everyday house use, as the heat pump already has the well pump cycling. If you used a Cycle Stop Valve with a small tank, the well pump would still cycle 35 times a day as the heat pump cycles. And while the heat pump is on, there would be no extra cycles for water used in the house, as the pump is already running. But the small tank might add a few cycles per day for house use during times the heat pump was not running. However, if the house is already using water when the heat pump comes on, or the heat pump is already running when the house uses water, it would cancel out a few cycles as the pump is already running. Overall, I would bet the CSV and small tank would not cycle anymore than the 80 gallon tank without a CSV, as has happened in many test conducted over the years.
There are a few other advantages to adding the CSV to your system, small tank or large. The CSV gives a mechanical soft stop at only 1 GPM. This eliminates any water hammer and greatly increases the life of check valves and other components in the system. The CSV would also deliver strong constant pressure to the shower. Of course, you would have to wait for the 20 gallons in the 80 gallon tank to be used first as the pressure continues to fall from 60 to 40. But as soon as the pump comes on the CSV would quickly fill the tank to 58 PSI and hold 58 PSI constant for as long as you are in the shower. 58 PSI constant makes a big difference to the shower pressure compared to when the big tank is slowly draining down to 40. You wouldn’t have to wait for the good pressure from the CSV when using the small tank, and the number of cycles per day would be very similar.