Is it possible for a single-class Eldritch Knight to learn Hex, or Hunter’s Mark, etc?

I am trying to build a singly-classed Fighter with ready access to a bonus damage on hit spell like Hex or Hunter’s Mark, but I’m not seeing many options for that combination.

While Eldritch Knight gives access to Wizard spells, Wizards don’t have access to either Hex or Hunter’s Mark. Nor does Magic Initiate (which would be easy to pick up with the Fighter’s ASI progression) allow a purloined Hex to be cast with Eldritch Knight spell slots — at least per my reading of the feat and this answer here, it’s once per long rest regardless of whether or not you have spell slots.

Is there some other way for an Eldritch Knight to learn some sort of damage boosting concentration spell along with their other spells?