I'm not seeing how the CoW principle undermines the universal representative principle. Could you elaborate? Paul said in the last verse of Romans 3, "..on the contrary we establish the law." If I understand that correctly, the law is in place as a standard of righteousness for Christ to fulfill as the last Adam. Thus is some sense there was in place a re-enactment of Eden in the new Eden, land of milk and honey.
Thus temporily, not for eternal justification, Israel My son, is the type of Christ undergoing and failing probation, whereas Christ as the last Adam does not fail.
The representative principle is that all mankind underwent their probation and fall in Adam. The republication theory, according to Kline, seeks to prove that Israel was under a covenant of works on the basis that Israel underwent its own probation and fall. The republication theory, thereby, undermines the universal representation of Adam. Now, if you would like to revise Kline's method of argumentation, and revert to a national probation that is different in nature to Adam's probation, then you are free to do so, but then you would not be holding to the modern republication theory. A different kind of probation would lead to a different kind of covenantal arrangement, and that would only serve to undermine the idea that "the covenant of works" was republished.