V2 speed is designed to provide maximum obstacle clearance at take-off with one engine out
I don't think so.
The OEM's interest is to sell aircraft and one measure of considerable importance is field length requirement which, in turn, is critically dependent on speed (V2).
The OEM will be looking for the minimum V2 consistent with Design Standards .. ie, driven by Vs or Vmca, although there may be some Type reason to go a bit faster.
Where does this leave us so far as obstacle clearance is concerned ?
(a) for close in obstacles, min V2 will give the best obstacle clearance as you can't go slower and any increased V2 will compromise the clearance.
(b) for distance obstacles, min V2 definitely is NOT the way to go - refer to the use of improved performance/overspeed V2 takeoff schedules.
Figuring Vx and Vy equivalents is straight forward but they are light aircraft considerations, not heavy .. the OEM/operator's ops eng folk will give you information regarding best climb rates.