The speed golf I have seen in real life has been disc golf stoke play, with a timer. Your time for each shot is the same, you don't have to hurry every shot per say, but at the end of the round, remaining time is given back as a bonus to your score.
Example: Nine holes, an hour timer, and 10 minutes per stroke. Some people were shooting 4-5 over, but sprinting through the course in 20-30 minutes...gaining 2-3 strokes back because they came in 20-30 minutes sooner than the deadline. Others were shooting even or under, but taking 45-50 minutes or more. The last time I played the winner shot +2 in 19 minutes and took it down with an overall score of -2 because he gained 4 strokes back for leaving 40 minutes of his time allotment. That's where the strategy and fun come into it.
Of course that example wouldn't work that well here, we don't have to run to the next shot! But something like that where the timer is totaled at the end and strokes given back for time remaining.