I'd argue that for a golf game, a "Maximum" Score run would actually be the minimum attainable score.
In my opinion, the concept of "Maximum" score from a vault standpoint is essentially the idea of the best possible score performance, not necessarily the highest numerical score value. In most games, that means the highest numerically achievable score. In others games though (some racing games for example) it may mean the lowest achievable time (which may be the best score performance for that game). Given that the best score performance in the rules of golf is actually obtaining a low score, it only makes sense to aim for the minimum numerical score value.
Besides, going for a high numerical value score in golf is actually intending to play poorly, which is somewhat contrary to the superplay idea of TASing in the first place. Given, as you've already noted, that the upper limit of score is capped at 2x Par; the maximum numerical value score can be clearly defined. But given the capped value, it also becomes trivial to achieve.
While it could be argued that whoever can get to that score the fastest still offers a competitive challenge, it still requires intentionally poor play. To achieve the max numerical score; one would only have to hit the ball out of bounds or into water hazards repetitively as needed to rapidly increase the stroke count, then make sure the ball is holed on the stroke that will yield the capped score value.
On a side note, while it can be anticipated that a minimum score performance in a golf game would also yield the fastest overall time, it is theoretically possible that a slightly higher than minimal score may be performed faster. For this reason, I believe that both a fastest completion run and a "Best Score Performance" run could be published side by side in the vault if they aren't the same run.
