As far as different strategies:
1) Take all the planets. As Chris said, this can take waaaay longer than usual and either lower difficulty or very smart play and/or favorable map (e.g. Snake). Basically the AI will continue to get more and more powerful to the point where you can feel pretty "railroaded" : either have a completely impenetrable defensive chokepoint or die.
2) Take 15-25 planets, accepting moderate spreading-out (skipping some planets). This seems to be the normal range, and the AI gets pretty dangerous by the end but not overwhelmingly so as long as you can defend your homeworld without having to simultaneously guard too many "chokepoints".
3) Take 5-10 planets, accepting major spreading-out. This can allow extremely-low-AIP games, particularly combined with long-range "sniping" of data centers and co-processors (the super terminal can be used to great advantage in any of these, of course). So much so that we introduced the Core Shield Generator mechanic to increase the minimum number of worlds that had to be captured before you can win. That can be turned off, though, which was a relief to several players who saw that as more of a "railroading". Even with them on, there's a lot of variation in other things.
4?) And that's just the question of how many planets you take; then there's strategic questions of what you spend your knowledge on, which planets you prioritize, and many tactical considerations on how you actually execute a given attack or defense, etc.
How you deal with spreading out is one of the points where strategies vary. I tend to play games where the AI launches a lot of exo-waves, so I just get used to the idea that any of my "outlying colonies" may get killed off on very short notice. I sometimes long for an "auto-re-colonize" feature because I keep rebuilding those planets, but it gets done and I'm able to make more progress, etc. And generally I set it up so that any AI attack gets "blunted" a little bit by each such planet it takes so that when it hits my serious defensive perimeter around my core systems there's much less of a threat left. Other players adopt a strategy much more focused on never losing planets. Other players never allow spreading out, though that tends to run high AIP.
Another point of variation is how to deal with the planets you don't take, and how to "manage" AI reinforcements. If you're going to skip a planet you can "neuter" them of guard posts to keep down reinforcements, at the cost of ship-time. That way any "reinforcement points" the AI spends on that world don't produce as many ships, though it can still hit the "population limit" for that world and start producing barracks and then carriers (but it's still easier to clean out). A more advanced approach is to keep some out-of-the-way cluster(s) of AI worlds on permanent alert to "siphon off" their reinforcement points to a part of the galaxy you aren't planning to do much in, and that tends to prevent the massive threat buildups and carrier buildups, etc, because the AI isn't generally hitting the "population limit" on individual planets. More generally, later on it can be good to have a lot of AI worlds on alert so the AI doesn't "chokepoint" you, or massively over-pile a world and produce lots of carriers. And, of course, one strategy on this point is to just not bother about AI reinforcements and use all the time saved thereby to go for a quicker win or some other advantage to make the win more likely.
A word about carriers: the AI needs a few counters to "impenetrable player chokepoint syndrome", otherwise a player can set up a nearly un-loseable situation simply by picking a map that lets them set up a one-world chokepoint and dump every turret/ff/etc in the galaxy on it. Carriers are one of those counters. Some chokepoints can melt even carriers, of course, but it tends to involve strategic opportunity costs from all the knowledge dumped into defensive types. Or superweapons, which have their own costs/tradeoffs.
Anyway, the main problem in your current game seems to be that you've gotten AIP higher than you're equipped to handle smoothly (armor ships are perfectly viable bonus type, by the way, but their strengths may not gel with what you're trying to use them for) . You said you're still making progress and you might still win, but basically you've fully woken up the bear and it's not happy
There are ways to face a grizzly hand-to-hand and win, and if you want to play the game that way you have to pick a strategy suited to that. Other strategies depend on killing it before it's fully aware of you.
As Cyborg said, you might enjoy the Fallen Spire campaign better than the "normal" game. Worst to worst, it's a very different way to play and win the game
Though you don't have to pursue the campaign to its "logical conclusion", and can still win the normal way, etc.