Interestingly, in Friedman's "US Destroyers, Revised" book, he describes how the USN lost interest in frigates in 1989 precisely because the "new" plan became to use older destroyers for any needed convoy escort. (In this case, that would've been the Spruance class.) So, the thought of building more frigates was abandoned. No mention on whether there was any plan to reclassify them. There doesn't seem to have been one.
This is all a little too much hair splitting as far as I'm concerned. But, technically, USS Slater is a DE--Destroyer Escort--and not a DDE--Escort Destroyer, which was something else. Despite that, I personally don't feel what you wrote was wrong. "Descriptive function" as opposed to "technical designation," and I am perfectly fine reading it that way. Quite close enough to make me happy!