Setting sag is great and the numbers given above are generic and just fine IMHO.
Flipping the eccentric at the top of shock does not effect sag. It effects ride height. Primarily it effects rake and trail (stability vs steering effort). It also effects center of gravity and chain line.
HP4's came with 200/55, others before and since 190/55. There are probably others that came with 200/55. BMW had a short list of compatible tires when the HP4 first came out and I don't think it has changed since. I think this goes more to incentive than anything else (measuring cost money). There are people far more informed about what BMW has done than I. The prevailing information suggested that it was not just the size (that is anything but uniform from tire to tire) but the profile (shape). For a given width the height will effect things again.
There are people here who are well informed and fast, experienced riders. Me...
I have a 2013 HP4 (now 10 years old). I have run OEM Pirelli's 200/55, Dunlop Q3+ 190/55 and now Pirelli TD SC3 200/60. The only tire on the BMW list that I have run, OEM Pirellis. I have not been disappointed by performance but maybe I haven't recognized the effects. I had to remove the hugger to run the Pirelli TDs because as karimak2 pointed out it was rubbing. It was so close everywhere that, even with significant modification, tire warmers were never going to fit. Pirelli states the diameter of the tire is 688 mm. That is 20 mm larger than their 200/55 tires. This puts the rear of the bike 10 mm higher. It was immediately noticeable. I have noticed the traction control and abs lights lit at odd times. Odd, because I was neither accelerating or braking hard at the time. This suggests to me that the electronics are not entirely happy with the tires. I don't have a camera and I am usually a little busy to try and sort it out. I have not noticed a performance problem in accelerating or braking but maybe I am just not skilled enough or fast enough. I don't race. If do encounter a problem, I will drop back to a 200/55 tire, but I like all the side wall. Even though I may not exploit it like others, it gives me confidence to push harder.
The eccentric is in the middle. I will lower the back end using the 1.5 mm eccentric that, to my understanding, will lower the rear anywhere from 3-4.5 mm (I don't know the linkage ratio). I experience some instability on the straight when the front end is light. Easing my grip on the steering takes care of this but it seems a little too prone to this.
The Pirelli TD SC3 200/60 are very tall tires, for contrast their 200/65 tires are only 2 mm larger. The difference in effective circumference when vertical compared to at the edge is significant. I estimate 10+% speed difference. I enter the straight at about 115 MPH on the speedometer. If measured by a GPS I believe it would be about 100+. Once stood up I think it might go the other way in that the GPS measured speed would exceed the reading on the speedometer. You can see this for yourself if you watch enough YouTube videos that capture the dash and have telemetry. You can also hear it when listening to the engine on a 600 with a fast rider where the engine will speed up at the apex and drop back as the bike stands up.