I don't think there is a 'simple and elegent' solution that will make doomstacks disappear without making some other element of warfare equally frustrating. What would be necessary would be a major overhaul of the entire naval system including a large degree of automation (in the way of hoi4) that doesn't currently exist withing the game.
I agree on the problem, I don't think forcing the player to split their doom stacks and micromanage more has any chance of being fun. On the other hand I don't think HOI4-ing it is such a stretch.
Fleets could be merged with armies and have "areas of operation" that function similar to sectors but are not limited to your territory. Within the AO the player will set some macro-priorities (e.g. careful vs risk-taking, aggressive vs defensive, conquest vs raiding, ect.) and the AI admiral can handle the rest. Then the AI can do all the things that are too much of a hassle for the player - dispatch corvettes to get sensor data and pinpoint targets/threats, dynamically split the fleet into task forces to hit stations, bombard planets, then unite them in time to meet an enemy fleet for a showdown. The AI can be much better at avoiding doomed battles, emergency-warping and canceling invasions to preserve your ships and armies.
So a minimalist approach to HOI4-ing it is basically copy/pasting the sector system for fleets and improving the tactical AI. (or maybe unshackling it cause I believe the current tactical AI is intentionally allowing its fleet to get wiped to appear more "human")
Coincidentally it could have positive effects on the core strategic game:
- fleet wipes / army wipes will no longer be as common, thus fighting a losing war will be feasible
- less micro means war no longer requires the player to be constantly focused on their fleet/armies during war, thus making long wars more feasible for the human player