while I built up 8 capital ships spread out over 2 fleets
Eight capital ships is serious overkill. Experience in battle is split evenly between capital ships, meaning the more you have the slower each one progresses. This means you'll have a lot of low-level capital ships, which is inferior to a few high-level ones. This is even more true for TEC than it is for other factions.
Capital ships have lots of selling points, but in terms of sheer damage and durability for the amount of money you pay they're significantly inferior to ordinary frigates. High-level capital ships with good abilities can be great in combat, but at lower levels they can be ignored. I wouldn't even regard a level 1 Kol as a serious threat, but a level 6 Kol can shred through waves of bombers with impunity. You need to balance them out with frigate power.
or just general advice on TEC vs. Vasari?
Make your push early. TEC is a rush faction that unlocks their best military units and upgrades with only three labs, and can get a wicked economy operational very fast. Vasari is very much a slow development faction with generally weak units, but if they hit their high-level techs they become a lot more difficult to deal with.
I've managed to make them retreat each time so far after a brief fight, but it's only a matter of time before they throw their entire fleet in that bottleneck system at one of my two neighboring outposts.
Easy solution is to throw down a starbase to secure your holdings. However, as you may soon discover, the "starbase leapfrog" tactic trivializes the AI. I find it much more rewarding to stay one step ahead of them with my fleet. It's challenging, it requires thinking one step ahead and proactively deploying my forces, but that's the fun of it (plus it better prepares you for multiplayer where human opponents will run circles around static starbases).