However, I don't like the idea of a fixed number of rebuilds required to gain control. In my opinion, this is only acceptable in a mirror match, where the maximum possible randomness has been removed, and the player who doesn't get a favorable starting position loses (I'm exaggerating for clarity). Fixed control could work here, and it wouldn't make things worse. In HotA+, random factors should not be removed (increasing the importance of the remaining ones), but rather added to, so that they are distributed more evenly. If a clear imbalance is found among the many random factors, it is more useful to weaken that imbalance than to remove it.
Therefore, I suggest once again discussing the possibility of limiting the use of spells by timing. In my opinion, this quite effectively solves the problem of weakening the imbalance and is easy to implement. It would also look more or less organic in the rules (a similar practice has existed for many years regarding the Grail).
Obviously, everything written above applies only to HotA; I'm not ready to participate in a discussion about HotA+.