Ok, well I've been playing against the comp for almost a week now and I think things have finally come together for me as the Vasari. Here's my new approach that worked really good last night:
-I start off with the 2 scouts and a colonizer at my frigate factory. I build a cap factory that makes the battleship cap and then I scuttle the factory (I used to always build the colonizer cap, but I am finding a high-level battleship to be much better in the long run on the maps I play). I build the mineral mines at my base. I build a military lab and an economic lab at my base.
-Meanwhile my cap and colonizer take over the nearby asteroid. I upgrade the asteroid and build the mineral mines and an economic lab. I upgrade my home planet (using the black market a bit) and research kanraks.
-Then I spam kanraks until I hit the first fleet limit and if I have another nearby asteroid or non-volcanic/ice planet I go take that over and upgrade it at least twice and max it when I am able. At this planet I start building military labs and keep building military labs at conquered planets until I get enough to research subverters.
-Meanwhile I am researching volcanic and/or ice upgrades so I can take those planets. I am also upgrading my fleet limit to spam more kanraks. Once I get 15+ kanraks I start upgrading their defensive/offensive capabilities.
-Once I get 5 military labs I research subverters and add those to the mix as well, continuing to upgrade my fleet limits as necessary. After 5 military labs then I go for 2 more economic labs to start getting a trade route going and by that time I have a large enough empire that a trade route makes sense.
-All this time I am trying to work my way toward the nearest AI and to figure out where the relevant choke points are. At the chokepoint planets I build defenses, researching repair bays and I put down a pair of overlapping repair bays and a turret or two. I also upgrade emergency defenses at the planet and send a small group of kanraks there. The goal is to delay an attack until my cavalry can arrive.
-Once I hit the point where I can't conquer any neutral planets anymore I build a cap factory and frigate factory at one of the chokepoint planets and get my siege cap built. I also continue to spam kanraks and subverters from my two factories (this combo does a surprising amount of damage!).
-Once my siege cap is built and arrives I invade the AI. Once their fleet is destroyed I may research siege ships (I know they're not loved too much on these forums, but they are handy for taking planets after a fleet has been eliminated). I will also research and start adding HCs at this point to bolster my fleet and will also add more caps as I am able.
-The final thing I will say (because the above pretty much summarizes how I have been able to now have success) is that I have also found diplomacy and pirate management to be important, especially when I have played against the hard AI. Getting dogpiled by 2+ AIs plus the pirates (happened to me one game) spells disaster. So, I make sure the pirates are attacking an AI that I want to keep off my back and I make sure to build relations with key AIs so I have some allies (note: I play 6 AI + me FFAs on large/single/random map). However, once I have a really strong fleet and am in good position then I'll let the pirates come for me if they want as I can handle them.
-And that's about it! I would love any feedback you might have. Since I'm a new player I don't expect this to educate anyone, but am mainly just posting this to get feedback. Thanks!