Took a look at things, the golems you have access to wouldn't help you much anyways (and I didn't realize you hadn't repaired them yet.)
You definitely play much differently than I do, which is sort of a given, since this can be played so many ways.
My suggestions would be as follows: Give up any border planets that aren't forming a highway to the core worlds or defending something important. You have no energy problems at all, so you don't need them for generators, and you don't really need the income either. This way you can focus a lot more turrets on the places you do need to defend. (Namely that factory and your homeworld.)
You should really get a scout on the planets you're trying to invade. Once you blow up the tachyon guardian even a single Mk1 scout can go in just fine. Though I'd honestly recommend researching the Mk 2's (I actually grab Mk3s for the convenience myself) since they're dirt cheap and you get way more of them.
I'd use your available knowledge (one planet isn't finished) to acquire Mk 2 engineers. Use them, along with mobile builders, to establish a beachead where on the planet you want to invade. Keep a half dozen on the safe side of the hole to rebuild more engineers quickly if you need to. For the beachhead, Build a planetary shield first (just to protect the engineers really) and then turrets. Heavy Beam turrets work best for this, I usually research them a lot, though they cost a lot of K. But even with just the Mk1 turrets you got, it's a significant help, and if you throw in a bunch more turrets, you can take a big chunk out of the enemy forces. Bring along your ship cap of mobile repair stations too. They're cheap, no reason not to.
While the enemy is swarming your beachead, have all your bombers fly around the system blowing up guard posts. Even if this invasion fails to control the planet, less guardposts means less reinforcements, so you can overwhelm them next time. It also means less guardians, and Mk V guardians can be a bitch.
Once you grab the planet you seemed to be working on, you'll have a bit more knowledge, I'd use it to get the next mark of heavy beam cannon. That'll more than double the output of those things when you got them all built. Also, Mk2 and above have radar dampening, which helps keep them alive a ton. You can use the Mk 2 heavy beams to take out forts by placing them in the sweet spot between their range and their radar dampening. You can attack the fort from within 30k range, the fort can only attack the cannons from within 12k range. Cannons have 14k range. Winning!