Action Points in d20 Modern

Part One: Dice ≠ Challenge. Part Two: Decisions = Challenge. Part Three: definition of issues 1-5.

Action Points in d20 Modern give a larger individual bonus and so avoid many of the problems Cyberpunk luck has. However, the default "points gained by level" option does hit issue 5. Since they give a bonus die, Action Points can sometimes have issue # 2, as well, but the multi-die scaling with character level makes this less problematic at levels 7+.

Perhaps ironically, you could increase the challenge to the player by increasing the rate at which Action Points replenished. A budget of Action Points per session would tempt the player, and empower them to have greater control over which rolls fail and which succeed. I'd suggest Action Points equal to 1/2 your character level (rounded up) each session, but with unspent points being wasted.

Full disclosure: I've only GM'd modern briefly, and it was several years ago. As such, I make no promises that the house-rule above works well with all possible Action-Point powered class abilities.