Track every hole, handle carryovers automatically, see exactly who wins what.
Each hole is worth one "skin." The player with the lowest score on a hole wins that skin outright. If two or more players tie for the low score, nobody wins.
When a hole is tied, the skin carries to the next hole. That hole is now worth two skins. Ties keep stacking -- a run of ties can make a single hole worth a massive pot.
You win a skin by having the outright lowest score on a hole. No ties allowed -- if two players both make birdie, neither wins and the pot carries forward.
Multiply each player's skins won by the skin value. Players who win no skins pay into the pot. The pot is distributed to skin winners proportionally.