Mm…you may want to ask among all “micro-level conditions” that you listed, which will no longer hold, if taking the Rotemberg frictions into account? 
(1-\gamma)\frac{\delta}{2}\left( \pi_{Ht}-\pi_H\right)^2Y_{Ht}
and
\gamma\frac{\delta}{2}\left( \pi^*_{Ht}-\pi^*_H\right)^2Y^*_{Ht}
that have Y_{Ht} and Y_{Ht}^* terms.
My thought: Nothing wrong, except:
\displaystyle \mathcal{F}_t = C_t + (1-\gamma)\frac{\delta}{2}\left( \pi_{Ht}-\pi_H\right)^2Y_{Ht}+\gamma\frac{\delta}{2}\left( \pi_{Ft}-\pi_F\right)^2Y_{Ft}
So I regard Rotembergs as “garbage” terms, and do not enter into any previous piecewise conditions.