As a 92A, what place of duty/position/role is there to work from besides the motorpool and the SSA?

I agree with MSG Livington, working with the S4 would broaden you. As a CPL I think you should not transition to the S4 as your life’s blood for now is unit level and you should strive o become an expert.

If you're looking for actual work relating to logistics...speak with your Commander to see if you can pull some hours every now and then working up at your BN S4.

I was in the same predicament as you, but unfortunately there's not a lot of room for growth until you pin SGT and/or SSG. Twice I had orders to be assigned in the SPO section and was referred back to the unit level because of I wasn't SGT at the time and lacked in-depth knowledge of Z Park manager roles.
My advice, look at going warrant if logistics is truly imbedded in your mind. Could also try checking in with your counterpart PBO, 92Y and S4 on their day to day and look at going SFAB. SFAB is looking for the most diverse 92A/Y when I went through.