Thanks for the thoughtful responses everyone.
It's reassuring to hear that the biggest concerns are things I've been designing around. Here are a few examples (feel free to dissect these remedies!)
Problem: too many points of attack for enemies. → Solutions: not only is there no perma-death (in fact the units are non-unique such that you can upgrade a "class" of unit and obtain multiples of that class), but the combat is very player turn focused. Basically the player is expected to lose units, and can replenish them when they do. It's also not exactly heartbreaking to lose a unit (the game takes places in the form of a wooden board game, so it's more like losing a pawn in chess versus watching Mia eat a crit for breakfast.)
Problem: too little predictability due to more movement options. → Solution: the player has nearly perfect information (no hit chance, no wacky AI; it's closer to chess in this regard as well). I like that people touched on the puzzle-like quality to FE maps, because that's one of my favourite things about them. Integrity mentioned a FE strength in "relative predictability in addition to relatively lower mobility", in that light I could describe this hex-based combat as even higher relative predictability to even lower mobility, since all the numbers are single digit and the typical base move is 3 instead of FE's usual 5-6 (I want players to not have to do too much algebra).
Another thing that I hope addresses the increased danger for any unit is that there are attack range patterns that limit total targetable tiles. Specifically, many high-range units can only hit on the "lines" of the grid (imagine an FE bow with 4 range, but it can't hit diagonals). The goal is so that the scarier enemies become manageable if the player uses the environment effectively.
All that might count as too mechanically different to be called FE-style combat, so maybe FE-inspired (FE-distilled?) is more apt at this point.