How do I Make this Backgammon-Spinoff more Level and Fair?
The easiest rule change would be to disallow hits made in a home board. Extending a nuance from this rule, would be to disallow hits made in a home board


unless they come from a point on the outer board or
only if the piece is entering the opponent's home board or
unless the roll is a double, then one piece may be entered on the point and make the hit


This rule and nuances create a catch up mechanism whereby the player on their march is not trapped by the opponent's fall, and the fall itself is also slowed by the points on the home board being clogged by singles.

Taking any or all of those extra details will have varying effect on this stage of the game. Given the proportion of games that would arrive at this situation, a significant amount of simulation or playtesting would be needed to determine which nuance(s) most accurately transfer the advantage held before this situation to the equivalent advantage held after it.