How to keep moving forwards?

[IIE16 Yoshi]

First things first, I have a lot of assists and make-it-easier things going on. Golems, a 10/10 Dyson Sphere somewhere, 10/10 Roaming Enclaves and the Fallen Spire. Also either a +100% or +200% resource handicap. I nearly have a full cap from MkI-IV of ships that the AI is regularly throwing at me due to choosing parasites as my first, getting one of the younglings later (never use the things, don't particularly like that they're pretty much always at half health) and then getting scapegoats. I was a little skeptical of scapegoats at first, but they have really helped to bloat the fleet. Many of the MkIV ships I have in the fleet are unavailable to me as the closest Adv Factory I know of is in the third quadrant. Here's the state of the map at the moment. Three Spire cities are up and I have room for a fourth inside home quadrant before having to move out. The next signal is at the chokepoint system of the second quadrant. All Merc ships are on the field.

I'm at the point that I keep reaching in my attempts to play this game. What to do next? You'll notice there's an empty nothingness to the right. I've been throwing my deathball of a fleet at the AI, crashing through repeated 1-2k garrisoned ships that are remainders of old Exo attacks judging by all the guardians and MkV ships I saw. Nearly every system in the second quadrant has a thing of some value on it. Design backups, MkV ships and turrets, golems and ARSs are sprinkled all over the place. I tried using a superterminal to lower AIP but that nearly hit the fan in a really bad way when I noticed a little too late that power surges were not large influxes of ships, but techups of the waves. Only got about 20 -AIP out of that. AI is gonna get really ticked off by ploughing through the rest of these systems, but my fleet tactics don't go beyond select all military, sit on top of enemy wormhole, view galaxy map, V-move into enemy system, wait a minute, AI's dead, Jim. But that's what I really wanna do with the Fallen Spire.

Sledgehammer through to Pushoyar for the Shard and just keep upping the arsenal of the Spire? Would it even be possible? I had the luck of the first three Shards all being inside home quadrant so the chokepoint bore the AI's assault. I imagine now being almost halfway to MkIII AIP, the assaults are gonna be a tad more vicious than they were at MkI AIP.

[Kahuna]

Always post a save file when you need strategy advice.

[IIE16 Yoshi]

1 save file.

[Kahuna]

The game is so laggy I really wanna punch a baby right now..
..anyway.

I'm not sure what's the problem here. You just use the Champion to get rid of they Nuclear Eye on the planet with the signal. Also I scrapped all of your defenses and rebuilt them properly so now you don't have to worry about defending. The defenses will literally auto stop everything. So simply go get the next signals. Although you could literally win the game right now. So you could just take your fleet and go destroy the AI Homeworlds. Just capture a planet every 4 hops to avoid deep striking, find the AI Homeworlds and kill them.

If you need to you can use Champion, Constituos, Spire Cruisers, Spire Destroyers and Flagships as a raiding group. The Flagships give the attack damage boost and the rest deal tons of damage. They alone can most likely destroy thousands of ships.

Just  send the Champion to destroy the Nuclear Eye. I mean literally attack the Eye itself and ignore the Guard Posts.

I've attached the save file.

[IIE16 Yoshi]

Problem was I didn't know how best to keep on going. Is it possible to clear every system on the way? All galactic conquest style?

EDIT:
I noticed you made a few edits and changes here and there. A couple extra controls were enabled and engineers were made to appear on every planet, other such things. Could you explain them for a guy that often abandons campaigns 5-6 planets in?

[Kahuna]

I repositioned the turrets and the Command Station on Boomthoway for maximum effectiveness and so that the wormhole to your homeworld is protected. Sometimes Exos have a bad habit of just ignoring everything and going for your Home Command Station. They can't do that now. I should have split the Minefields between all of the 3 wormholes though.

And yes I changed some of the global controls. Click the CTRL button in the lower left corner. The options are pretty much self explanatory. Just mouse over them and read the descriptions. What settings you want to use also depends on your preference.
Auto-kite behavior should always be enabled. So the value should be lower than the range of the ship with the shortest range. Just set it to anything between 0 and 1000 and all of your ships will auto kite.
I've set the Engineers Do Not Assist Large Projects value to 451 because building a Mark III Engineers costs 450 metal per second. Which is one of the highest values in the game that still doesn't wreck your economy. So with the value set to 451 Engineers will assist the building of Mark III Engineers.

I enabled "Allow Roaming Enclaves To Attack Independently" because you have set Roaming Enclaves to 10/10 which means they could probably clear the AI Homeworlds for you.

I also sent scouts to the near by planets to see where the Exos and CPAs are coming from. Also I just like to know whats going on around me.

I forgot to build Space Docks and Starships Construtors on Boomthoway so you should do that. And I say Boomthoway because it's closer to the front line than your homeworld so your reinforcements will arrive faster. I always build reinforcements in the front line.

So..
-Get rid of the Nuclear Eye on Pushoyar and then the signal-
-You have forgot to destroy the A-Core Shield Generators on Vercaveburn, Yolik and Marex.
-Destroy the near by Data Centers.
-There's a Mark V Plasma Siege Starship Fabricator on Chuna and a Mark V Leech Starship Fabricator on Misi so you might want to hack those.
-You can also hack the Advanced Factory on Kobanzub and the Advanced Starship Constructor on Leael by capturing Chuna and then hacking them.. if that's what you want to do.
-But once again: your fleet and defenses are so strong you could finish the game right away.
-You don't have to capture every planet on the way. Just capturing a planet every 4 hops to avoid deep striking is enough. If you're good a planet every 6, 7 or 8 hops is enough. And those planets you capture can be kind of expendable beachhead planets. You don't need to care if you lose them since they're expendable and you can just capture them again. They can be used as staging areas when you attack the AI Homeworlds.