Have you never watched biathlon? The rules speedgolf needs are already there for us to see. In biathlon, for each missed shot, you ski an extra loop of 150m before leaving the shooting range area. This means it’s still all about whoever gets across the finish line first (in the shortest time), and nobody cares if how many targets you missed, as long as you missed fewer than the competition, or made up the extra loop distance faster than they did the 5km laps between the shooting.
So for speedgolf, we can treat each hole, or set of three holes, like a biathlon lap plus a shooting.
Each hole has a par. For each stroke above par, you have to run an extra loop of about 200m. These loops could be done between every third hole, and you run all the loops you must before moving on to the next hole. So between hole three and four there would be a 200m loop. If you complete hole one below par but hole two above par, and they equal out, you don’t have to do a penalty lap. This means below par shooting is still encouraged to “bank” some shots to use up later if needed.
In biathlon, you sometimes get a few extra bullets, so if you miss one of your shots, you can spend those bullets to reduce the time spent doing the penalty loops. It takes some time to reload the gun, but it’s less of time penalty than a 150m loop.
Speedgolf could have three “free shots” that you can take at some point around the course, which you could save in case of really wayward hits.
The length of the penalty loop could be adjusted, of course, to balance for golf skills vs running speed, but both would still be dependent on each other.
The issue with having to do a penalty loop after the 18th hole would be the that final moment would be running across a finish line. This wouldn’t do at all! The game must end with the ball going in the hole!
So I propose there being a loop at the end of the 17th hole, where you get all your previous penalties out the way. Then there would also be a penalty loop right at the 18th green! If you reach the green at one below par, you just go for the putt, or first do a penalty loop for how many shots above par minus one.
Then for each miss on the 18th green that puts you above par, you have to do a 200m penalty loop. This means that your clock stops the moment the ball goes in the 18th hole, and no matter what, you don’t have to do any running following that moment.
By the way, biathlon is super fun to watch. In Germany it’s way more popular as a spectator sport than golf, as far as I can tell. The balance of ski fucking hard mixed with can you get your body calm enough to do precise target shooting is a really cool concept.