I was able to code the "beat" mechanic I decided upon. The idea is that once both players lock in their move (strike, grapple, block), the game chooses a number of "beats" a player has to win (3, 5, or 7). These "beats" are the reaction game mechanic pieces. If a player wins the majority, then they get to execute the move they chose in the beginning. This is also where the rock-paper-scissors match-up happens.
I decided it would take a Pokemon-like buff/debuff in that in the example of grapple > block, the grapple would do 1.2x damage. In the example of grapple < strike, the grapple would do 0.8x damage. In the example of grapple == grapple, it would do a straight 1.0x damage. Or, you know, something to that effect.