Trap bar won't really do the trick from what I've seen. The issue is that the weight of the car is behind you, whereas the trap bar has the weight beside you. It really is a different animal when you play with the leverages. I would definitely try out the ghetto rig when you get the chance to see how much it sucks, haha.
If the truck pull is an actual harness, you want to get yourself some rock climbing shoes. Nothing else will grip the floor better than that, and you need that to break the inertia of the truck.
For conditioning, the best thing I can do is the events themselves. It goes a long way toward quickly improving your conditioning since you develop some specificity and skill/efficiency in the movement. Instead of having an events day, I like to work an event or 2 into my training, usually as a means of improving a core lift.
I'm not sure what your training is like, but say you were doing something like 5/3/1
-Bench (if you really want to go hardcore strongman here, you could make this incline press instead)
-DB press (clean each rep)
-Squat (a lot of folks like front squats for strongman. I don't ever do them, like the Safety Squat Bar more, but something to consider)
-Press out of rack (competition style, 60 seconds)
-Some sort of strict pressing
-Deadlift (I would consider getting better at conventional leading up to the comp)
-Stones/truck pull (alternate each week)
Start lighter than competition weight and try to develop some technique/conditioning at first. As you get closer to the comp, you can increase weight until you're really dealing with comp weight for comp time. Additionally, instead of doing sets of reps, you can work in sets for time as your assistance work approach and get used to operating in that style.
If you have time/energy for cardio, there is of course other things you can always work in. Dumbbell cleans tabata style, or 3 reps every minute on the minute for 10 minutes as an example, pushing a prowler/pulling a sled to help with the truck, just some general stuff.
You're in a good position knowing the events so far out. I'd get in touch with the promoter and make sure you can get as much details as possible.