V2 overspeed still doesn't take you past Vx. That method is used in jets (where Rwy length is available) to get closer to Vx for the climb.
I use the rolling start from downwind taxi a lot ie power applied as I turn the corner from one side of the airstrip.
The goal is to accelerate & rotate to achieve Vx then flap & gear as soon as possible. Maintain Vx & full power until clear of the obstacle. Some strips I go into require a turn almost as soon as airborne.
If a soft, boggy or rough field then that will adverserely affect distance required. No getting around that. Get the thing airborne in ground affect as soon as you can - but not below Vmc - then accelerate to Vx & as per before.