Build up your grip by doing pull-up hangs with a weight belt on. Also, walk around the gym with the heaviest dumbbells they got.
Do front holds for time with a plate.
Do dead lifts with a weight you can get 10 reps with and try to crank out 20 (preferably with a trap bar).
Buy a keg of beer and press it overhead. Fill it with sand instead of water if it gets too easy.
Don't tell me there are no empty bags or sacks you can fill up with shit to do loading.
That's stuff you definitely CAN do to simulate events.
The thing is, 5/3/1 isn't a good program for a Strong Man who doesn't do event training. You need to go HEAVY without much warm-up in order to simulate a competition.
So since you haven't started training yet, I would advise a heavy, simple program of 2 training days featuring the most important exercises for strong man (front squats, dead lifts, curls, overhead press) and actually making an effort to drive a bit to train at a strong man facility (I travel around 3 hours every time I go).