Prioritize work by ROI and alignment with the institution's mission, communicate the prioritization to relevant decision-makers in your management chain, and actually follow through on it unless coerced otherwise.

Edit: There's no guarantee this will work out positively—nothing is guaranteed—but it's worth considering if the alternative is giving up / changing careers.

just enough to get yelled at, but not enough to get fired. Be an annoyance to deal with, by towing the line.