So far I haven't made any nerfs for Han, but I can certainly see the issues you mention @hamdich. In addition, I think crossbows are a little bit overtuned, they probably need at least slower prepare time.
I agree it is difficult to balance sword cavalry in p1, it may be the best choice to move them out of p1.
As for acceleration and spear cavalry, I see the concern about spear cavalry having a hard time chasing. The first thing to note is that spear cavalry have 2 components that make chasing difficult: 1) stopping to attack and having to accelerate and 2) prepare time. Prepare time is a massive contributor because the spear cavalry must be stationary during prepare time. I actually have what I think is a nice solution to this, if people are interested.
among my list of "unit specific upgrades" (see attached discussion) are 2 upgrades for spear cavalry:
1) Horse Racing: increased movement speed and much higher acceleration (phase 2)
2) Lancing tactics: increased pierce damage and decreased smaller prepare time.
after testing, these changes made spear cavalry much more effective when chasing enemy cavalry, and the distinction is that these upgrades are unique to spear cavalry, so the upgrades act to differentiate spear cav nicely.
I have not yet made a merge request for these upgrades (https://gitlab.com/real_tabasco_sauce/0-a-d-community-mod-unit-specific-upgrades/-/tree/unit_upgrades), but I think they should be added to the community mod after balance changes and team bonus changes.