any decent track hub has serrations on the lock nuts and on the axle nuts,
it doesn't matter which way the drop out opening is oriented, because your probably never going to have the axles resting on the closed end of the drop out due to proper chain tension. also, when you tighten one side, it would want to slip towards the front, and on the other it would want to slip back, (you tighten to the right on each side) but the serrations prevent this on a properly spaced frame for your hub.
the phil woods style use an allen head bolt with a free to rotate serrated washed riveted on just like a true track nut. it works well,
to the point, no you don't need track specific dropouts for any track hub i've ever seen, they all work the same way.