Maximal eventually different families for uniformly weak Ramsey ideals

We study $\mathcal{I}$-maximal eventually different families of functions from the set of natural numbers into itself where $\mathcal{I}$ is an arbitrary ideal on the set of natural numbers that includes the ideal of all finite sets $\mathrm{f}\mathrm{i}\mathrm{n}$. We introduce the class of uniformly weak Ramsey ideals and prove that there exists a closed $\mathcal{I}$-maximal eventually different family if $\mathcal{I}$ belongs to this class; this is the case for arbitrary $F_{\sigma }$ ideals and Fubini products ${\mathrm{f}\mathrm{i}\mathrm{n}}^{\alpha }$ with $\alpha <{\omega }_1$.