This is one of the reasons I turn off tech trading (for lack of any other acceptable to me options) - the extremes you can go to with tech trading/selling and the collective research the AIs do similarly is unbalanced, IMO. Going with lots of minors makes it even more abusive. Tech trading off also somewhat affects the pace of the game since you can't leap ahead in every tree branch via trading.

I colonize aggressively and don't let planets sit empty, but I also don't overdo it and don't feel the need to build out every tile til my econ stabilizes a little.

Map size might be a factor. I usually play medium or large with default settings so usually between anomoly cash and population catching up with limited colonization I can usually stabilize my economy before things get out of hand.

I do usually take an econ bonus for my race and pick federalist party though to help.

I never depend on trade but it can be a nice suppliment while you build up.

In DL I would often research towards and create survey cargo ships to further rake in the anomoly cash but it's kind of cheesy and I haven't bothered trying it in TA.

Yeah, thats one of the first strategies I discovered too, and quickly became bored of it. It really felt dirty, somehow. Set up your race with as much research and diplomacy bonuses as possible, research like crazy and sell (almost) all of it for gobs of cash. When an AI researches something useful, buy it and then sell it to all the other races: basically making money out of thin air.

Like I said, it got a bit boring and unrealistic. Lately I've been on a more economic path, maxing out Economics and Population Growth, with a bit of Morale thrown in.