I would keep your event training seperate from your gym work, with the exception of conditioning and pressing work since neither of those will be overly taxing on your body or CNS.
For a beginner strongman sometimes they can benefit from additional event work with very light weights but it will have to be very carefully planned and monitored to avoid overtraining.
With regard to squatting, Front Squats are definitely going to have more carryover to strongman events. I would not necessarily go ahead and eliminate exercises but I would start off with Front Squats and then do ATG, Power, or Box Squats as a secondary movement. There are some very good strongmen who squat frequently and others who almost never squat. A lot of it depends on your squat technique since a wide stance powerlifting squat really has very little (if any) carryover to strongman.
I wrote an article on putting together a strongman training routine that you may want to take a look at:
There is also a strongman gym training program that I created for another individual posted earlier in this thread.
Let me know if there is anything else that you would like to brainstorm.