I recently dropped to 360, the lowest I've been in a long time. I'm back above 400 now and will likely earn more than I place for a while. It was an unusual set of circumstances relating to the new TB making a bunch of previously irrelevant characters more relevant and also throwing zetas on the new tuskens. But it does happen that I go through periods of using more than I'm accruing.
Generally I don't drop zetas on a character until g12, though there are exceptions. The Tuskens are a classic example of this b/c their use in Galactic challenges made it much more important to drop a couple zetas on them now, at sub-7* and sub-g12, to meet my GC goals. Or at least to meet them with minimum stress.
Any policy should have some flexibility built into it, but if you don't zeta toons before they hit g12, that will make things much easier for you. It will automatically weed out some toons as "not ready" and thus slow down the excited zeta dropping that can happen when several characters are released close to each other.
As others have said, it's also useful to limit your resources to a single toon or faction that you're developing. This would include zetas -- but even if it didn't, it would include them by accident if you apply my previous suggested policy b/c if you're only spending gear on a particular toon or squad, then you would only have a few toons at a time reaching g12 and thus being considered worthy of a zeta.
I doubt that things will be the same for you as for me. I've been swimming in a couple hundred zetas or more for years now, but if you started the game later than me then you have more previously-released toons to catch up with. And though I've used my g12 test for a long time, with gear acceleration that's more like how a g10 test might have functioned 3 years ago.
But even if things are different and even if I'm not able to tell you exactly when thing will get easier, I can assure you that they do. In fact, with the release of Omicrons, I'm convinced that they're going to allow even more zetas into the economy at some point before the end-of-year, possibly when they release the new Krayt Dragon raid, or possibly in conjunction with some as yet unknown changes to the game.
Be hopeful! The zetas will get easier and then you'll only have to worry about gates on Omicrons, Kyros, Signal Data, and relic mats!