Fast forward three weeks. I connected a Carbtune Pro to the throttle body and the picture before tuning is attached below. The connected cylinders are 1 through 4 from left to right.
Conclusions I had at that point:
1. My crude synchronization of starter valve #1, including tuning by ear, actually worked better than I expected.
2. I now (then) needed to synchronize cylinder #3.
I adjusted the starter valve of cylinder #3, assembled everything back, and was quite happy with the outcome. The cold start on the following morning was unusual. Started at about 1400 RPM, went down to about 700-750 RPM when engine temperature got to one bar, and up to a normal 1000 idle when the engine temperature got to 2-3 bars. It was not the thermal valve, since the thermal valve worked fine before tuning. No error codes was picked up from the map sensor either. When warm, everything worked nice and smooth. It was all about tuning, but it took me two additional weeks to come up with a possible reason.
One possible solution would be to tighten the nut on the thermal valve rod, but it is preset from the factory and instructed not to be readjust. The alternative solution was to tighten all the starter valves at the same amount, which, for cold engine, would give the same exact effect as tightening the thermal valve nut (the starter valves are tightened in the opposite direction to the thermal valve nut on the same plate). For a warm engine it doesn't really matter, since a different mechanism holds the idle RPM.
I tightened all the starter valves 4 clicks, whatever displacement this may result in, and double-checked with Carbtune that the vacuum readings on all cylinders is the same. Now the bike works like new, cold starts, warm starts, runs smoothly, and all is synchronized.
My additional conclusion:
Starter valve #1 is indeed calibrated to a specific length and not arbitrary locked at some generic position. It either has to be calibrated with the extension of the thermal valve rod, or with the specific throttle body after the thermal valve is hooked to it. It may be that for this reason, starter valve #1 is not sold separately from the throttle body. Either way, with some patience, it can also be tuned.