Your AIP total isn't at all too high. You've actually been pretty conservative compared to a lot of new players. Which is good for you. The downside is you've take a long time to get there so just the time along has given the AI a lot to work with. That said, hopefully some of this will help:
Any capturable structure switches to your ownership once you build a Command Station in that system. This means just destroying the enemy Command Station won't switch it, giving you time to finish clearing out the system before that structure becomes a valid target for the AI. Of the structures, Advanced Research Station is the least location sensitive since 1) it is mobile, 2) the second you capture it you get a new ship type unlocked (at random, Mark I and II of the ship type) permanently. Advanced Factories are more of a structure you want at least one of, but more are less valuable. They let you make Mark IV fleet ships of any fleet ship you've unlocked Mark III on. So it is really nice to have one, but more is so-so, especially those that are hard to defend (Advanced Factories aren't mobile). Be really aware of what ships the AI has that ignore Force Fields because it really likes to use those to assassinate Advanced Factories when you aren't paying attention.
If you are 19 hours in, a lot of the AI worlds are probably starting to fill up. Have you been getting messages about Barracks being created on AI worlds? This starts to make things really tough, but not un-winnable. The basic challenge you have at this point is getting stuff done between waves. You need to set small, obtainable goals and get to them right after you stop a wave. Pay attention to when the waves happen (there are two on separate times, so they can come at nearly the same time, or very staggered). If I recall correctly, waves are about 20 minutes apart but have a reasonable plus-or-minus each time so it isn't a fixed pattern for the whole game. On difficulty 7 it is a bit lower than 20 minutes but I can't recall the formula at the moment. While all that is happening, you've got a 2 hour window between cross-planet attacks. Remember, part of the time after each wave will be spent rebuilding what you've lost. So better defenses effectively give you more time to go on offense. Consider also that turret deaths are better than ship deaths because if you have very light ship deaths to replace you can go on the offense very quickly and let your remains rebuilders fix you defenses while you take an important objective.
As for cutting down what you are facing:
1) Waves and Cross-Planet Attacks are based on AIP, so the only way to make them smaller is to have less AIP. So reducing AIP through data centers will make waves smaller, and reduce the number of reinforcements being added. It won't do anything to ships already in play (or waves that are already incoming).
2) To have less enemy ships on a planet, you need to remove guard posts. Each planet has a "cap" that is based on the number of guard posts, so you can reduce the total number that planet will hold by killing guard posts. However, the ships do go somewhere, so all you are doing is shifting ships from that planet to elsewhere.
3) In the galaxy map, use the "Threat" option from the drop-down box at the bottom to see where ships are built up that might attack you. "Threat" are ships that you've pissed off but not destroyed and they are actively trying to find a weak-point in your defenses to attack. They will often join in with a wave to overwhelm you, so they are something you need to clear out if possible. Of course if you stir up more threat killing existing threat, you aren't really making progress. Note that you need a scout in the system (maybe a non-scout ship would work, haven't tested) to see threat on the galaxy map. So get scouts on all adjacent systems so you can monitor large threat build-ups. Even without scouting however, you can always see your total threat in the top bar so that gives you a good idea of how much bad stuff could be coming your way unexpectedly.
At this point you need to get the entire map scouted so you can identify all the targets you need to hit. Use Raid Starships to kill Data Centers and other AIP reducers if possible. If you have a Super Terminal that you can reasonably capture, that might work but you'd want to time capturing that system for right after waves. You also need to knock out the Core Shield Generators (if you have them on). After that it is all about planning you attacks on the home worlds. You need a path with no more than 4 enemy systems deep (or the AI will react to your "deep strike" by spawning extra ships). So the easiest method is to capture all the planets leading up to the AI world, but if that path is too long you might need to use a different technique.