I really like fighting the Threat, personally. They're cool guys. I especially like that the Hives do these periodic swarm storms at long range; reminds me of the days when Pilums would fill the screen. But they definitely have some frustrations.
Re: the Overseers. They've got the armor of an Enforcer and the speed of a Hammerhead, and never stop whipping what's effectively an ion beam at you. Their shields are inefficient but they don't have much else to spend flux on. (Well, kinda hard to tell if the Lash generates flux.) Yeah, they're difficult targets. While its not necessarily the case that the Threat should be solved by learning to just shoot the Overseers, its kind of annoying that you effectively can't interact with this mechanic. It's simply impractical to ever kill the Overseers first, such that its meaningless outside of lore/aesthetics that they activate ship systems for the other ships.
One possible way to make that work is set it up so Overseers don't get fabricated at all. A Threat fleet has as many Overseers as it starts with. In that scenario, they might be hard to kill, but every one you nail attrits the effectiveness of the entire Strike. On the other hand, it'd be kind of lame if none of the Threat could activate their systems anymore. Maybe something like they are very, very slow to fabricate compared to other ships. Another option is to make Overseer fabrication part of scalable difficulty. Imagine two kinds of fabricators; the regular ones can build everything except Overseers, while the 'pristine' fabricators can build Overseers as well but only show up in Third Strikes. Second Strikes would have to make do with the Overseers they start with. Tie the highest end Threat loot to those super fabricators and you got your risk:reward right there.
I haven't had as hard of a time dealing with the swarms returning to the fabricator as a lot of people but it is pretty impressive how hard they are to kill. It doesn't help that usually a destroyed ship is trying to back off, so their wreckage naturally floats back towards the fabricator, and then the swarms form on the far side of the wreckage. I often up end literally chasing wreckage with movement abilities to set myself up to take out the swarms. Also, perhaps the reason 1-fabricator fleets are disproportionately difficult to deal with is that all the newly spawned ships form literal walls around the one fabricator rather than being spread out among multiple ships, and the wall just gets replenished very quickly if you destroy a ship under construction.
One thing I'd add is that it's very frustrating to go looking for Threat and jump into 4 systems and not find any. I realize there's a system in place to force them to spawn eventually, but when even the Neutrino detector is hitting you with false signals in there, it feels more tedious than it should be.
Feels like sometimes they just spawn too far away. I've found Threat that didn't show up in initial pings by doing an active scanning pattern around the rock. Although maybe that's the system you are referring to, I'm unfamiliar with it.
As for the overall design of the Threat, I don't have the same experience as you guys do. I agree that it's a bit of a DPS check and you need to be reasonably aggressive against them, but the Threat being way more passive and slowler than the Remnants, I found that they allow more freedom for building your fleet. The Remnants, being very fast, suicidal and their strength coming from their raw stats and AI cores, are far more of a DPS check than the Threat. And I do appreciate that, for once, a player-piloted Afflictor is not an easy solution to a fight (it's still viable, but it requires better piloting).
Idk, Assault Units are a pretty straightforward DPS check. You will eventually get attrited by them if you can't either destroy them immediately or have the ability to press in on the fabricator. Or maybe if you're only fielding ships that can shield tank them through a whole Incursion Mode activation.