Measuring with an aquarium test set using drops.
I emptied the machine and filled the HX and boiler with tap water.
I collected water from the group head and from the hot water tap after the machine had been idle for 1 hour, throwing out the first bit of water that was in the lines and without using the pump. Steam boiler max was at 1.25 bar and group head temperature was at 210F when I collected the water.

Above I say that the boiler water was at 8 KH but that is wrong. I measured the boiler water again later and the KH drops by the same number as the GH, I believe that is to be expected.

Today I measured the boiler water again after the machine was on for many hours. The GH had now dropped to 2 dH. So I wonder if it just takes many hours before the equilibrium is reached.

Okay after some more measurements, I can answer my own questions.
It is indeed the case that it just takes a long time, like 4 hours or more, before scale starts to form if the water hardness is just above the equilibrium.

I had filled my boiler using water with GH of 2 dH and KH of 8 dH and then filled the reservoir using water with GH of 5 dH and KH of 8 dH.

Then I waited for a day with the machine turned on and pulling a few espresso shots every now and then, no hot water or steam was used from the boiler during this time.

Afterwards I tapped some water from the boiler, group head and water tank. The result was that the water in the boiler had dropped by about 0.7 dH in both GH and KH, while the group head water still had the same GH and KH as the tank water.

My boiler fills up with 0.8 liters of water, so during this exercise about 0.01g of scale has formed inside the boiler. During normal use of course, only small quantities of water get added to the boiler during the auto refills. I guesstimate that 5 auto refills with the harder brew water will also deposit about 0.01g of scale. So with an average of 4 auto refills a day, de-scaling once every 2 years should be enough.

For the brew water I did not measure any drop in GH and therefore no scale has formed. I will try straight tap water next with a GH of 8 dH and see if that gives a drop in GH from the group head. If the drop is not significant, I might just be able to choose the hardness I want based on taste and still only have to descale the HX only once every 2 years.

I still don't think your experiment is structurally sound and would not ignore Jim's charts. However, do as you wish and I hope you the best. You can reduce the alkalinity a bit by just adding some RO or distilled (ZeroWater) water.

Like I said, I defer to anyone with more HX knowledge.

If the water going into the machine has the same GH as the water going out of the machine, then no scale has formed, regardless of the KH values. There is nothing here that contradicts Jim's water FAQ. This holds for any machine, not just a HX.