As far as I`m aware there is nothing wrong with using a smaller vehicle, just comes into movement orders sooner, due to narrower base vehicle (eg a 2.9m load on a 2.5m truck bed, 200mm over hang each side, no order needed, a 2m wide deck with the same load would have 450mm over hang each side, being over 305mm over hang brings it into movement order).
The 3.4m roof is going to be a movement order what ever it goes on, on both width and overhang so you should be OK.