I notice that the minimum state of charge parameter affects parameters of the battery kinetic model, but I cannot see in HOMER help in what way.

The apparent effect of the battery minimum state of charge on the kinetic battery model constants is interesting and surprising.

When you change the minimum state of charge in the Create New Battery window, HOMER recalculates the suggested lifetime throughput and the kinetic battery model constants.  The process of finding the best-fit kinetic battery model constants involves randomness, so you can get a different result each time you do it.  Until now, I have never seen significant variation in the results from one time to the next, but for your battery, the results vary significantly.  I think that is just because HOMER can't find a set of parameters that fits your battery well, and every time it tries, it comes up with a new set that roughly fits the battery, but that is quite different from the previous set.

The minimum state of charge does not affect the kinetic battery model constants.