A big difference between hypergammon and backgammon is that there is little blocking in hypergammon. To rectify that, I have been thinking about a game I call "blockgammon".
Blockgammon is just like hypergammon with one additional rule: When you make a point, you actually block five consecutive points instead of just one. For example, if black has two checkers on his 6 point, those checkers block white from landing on (or touching down on) points 4, 5, 6, 7, and 8. His two checkers effectively make a 5-prime.
The idea would be to create a possible "perpetual double" position, like this,
where the chance of the position repeating is so high that if both players double on their respective turns, the equity at stake grows out of control.
Since blockgammon has just 3 checkers per side, the same as hypergammon, I could try to calculate cubeful equities for that game and see what happens.