This needs further investigation.
The basic idea is that both ModifiedEquinoctial and HyperbolicAsymptote use the RadPer parameter as an element.
But, given the same input state, setting RadPer in ModifiedEquinoctial gives a different final state vs. setting RadPer to the same value in HyperbolicAsymptote.
This is incredibly confusing, because it means that a state definition in initialization (where it's going through HyperbolicAsymptote) will give different results when copied to the mission sequence (where RadPer goes through ModifiedKeplerian).
The results match STK in both cases, so the math is being done correctly. It could be that RadPer just means different things in each state representation, and so maybe should not be shared after all.
More work is needed to understand the underlying cause.
The attached script illustrates the problem.