Mazur-Tate elements of non-ordinary modular forms with Serre weight larger than two

Fix an odd prime $p$ and let $f$ be a non-ordinary eigen-cuspform of weight $k$ and level coprime to $p$. Assuming $p>k-1$, we compute asymptotic formulas for the Iwasawa invariants of the Mazur-Tate elements attached to $f$ in terms of the corresponding invariants of the signed $p$-adic $L$-functions. By combining this with a version of mod $p$ multiplicity one, we also obtain descriptions of the $\lambda$-invariants of Mazur-Tate elements attached to certain higher weight modular forms with Serre weight $<p+1$, generalizing results of Pollack and Weston in the Serre weight 2 case.