Is this how some of the more advanced chess engines work, or even the not so advanced ones, where there's a point at which it stops searching the forward move tree in greatest depth, and instead starts searching backwards from a handful of plausible (gross move limit-bound) checkmate states looking for an intersection with a shallow forward search state?

Kind of, but it's calculated offline and then just accessed during the game: https://www.chessprogramming.org/Endgame_Tablebases