So the point of contention is can they move away to stop being an overlap and then turn

I still don't believe so - no.
Page 82 - 1st sentence - BGs can only move into contact as an overlap in the manoeuvre phase. And then later it states that 'Any other contact must wait until the next impact phase and is initiated by charging.'
Page 84 - side edge to side edge contact - "If not eligible to fight as an overlap they can can engage in melee as follows:" But they are eligible to fight as an overlap so they cannot move into contact.
I believe the most effective moves open to them are to contract into a column so that they contribute 2 bases to the melee. Or to move beyond the enemy, turn and do a rear charge in their next turn.