1. They actually cannot live on Earth for extended periods of time

Your premise is that Earth should be a candidate, since:

"[...] some have been on Earth for 20 years. [...] Clearly they're capable of living on Earth for extended periods of time, but for the story I need them to have ruled out Earth as their home the moment they arrived. "

However, you seem to be ignoring their alien-ness and looking at things from a human perspective. I propose they're not capable of such feat, and there could be several reasons why this is so, I'll try to brainstorm some.

Living here would shorten their lifespan

The 20 years they've been here, in their perspective, is a very short time, and the ones who are on Earth are committing an act of self-sacrifice. It could be that oxygen/water/sunlight/some form of radiation common around the Sun's class of star, but uncommon around other classes (call your astrophysicist buddy, maybe he knows what it is) causes their bodies to deteriorate much faster than they're supposed to, and in less than a century, they will die a heroic death. A mere century, I say, for a species whose usual lifespan is measured in millenia!

If you need a motivation, think of humans who volunteer for disaster intervention in high risk areas. They know it'll shorten their lifespan and they'll do it for the greater good. Perhaps they're already very old. Or they're convicts who expect their lifespan will be shortened much less than their sentence.

Earth is almost perfect—if it only had some unobtainium

Even though a small colony can live in Earth perfectly, their technology needs an energy source much larger than anything available on the Solar System. Perhaps they'd require a star with much higher energy output than the Sun, around which they can build their Dyson Sphere. Or perhaps their technology relies on some type of natural resource that isn't abundant on Earth. Maybe they're not even looking for a new planet to live in, just one to mine.

They're prospectors, Earth failed the test

Perhaps Earth was their initial candidate—or one in a string of planets they're visiting. And it failed some test. Perhaps they detected some natural catastrophe that would happen too soon to make the trip worth it, like the cooling of the core, or the death of the Sun, but they had to run a test in loco to be sure.

Maybe humanity didn't even exist before they came. Once they realised they couldn't colonise, they just seeded the planet with literal "bots", and our concept of history is part of the process: implanted memories necessary for the algorithm to run. Mere code.

Earth is too small

Maybe their species is so numerous that the planet's surface simply isn't enough. Perhaps their home planet didn't have so much water, so it could fit a lot more people comfortably (c'mon, over 70% of the surface? Who even needs that much water?).

Earth is too dry

Or maybe it's the opposite: Earth doesn't have enough water. How could they have guessed that less than 3% of the water would be fresh? Their most pessimistic models predicted 10%, this is unheard of, and the investment to desalinise this much water and bring everyone over is just untenable. Back to the drawing board.

They haven't actually been down here

We're talking about a species that can remotely harvest our brainpower for their own purposes. Why would they even need to come down here? Perhaps they have synthesised human-looking fleshbots that they can control remotely to do their bidding—like deploying the thought-harvesters and relaying the data back to the mothership.

2.They've already found a better place

You said it yourself:

Their system of FTL travel requires nearly perfect accuracy in terms of coordinates, so they're running simulations to be absolutely certain the next planet they reach is habitable before using up expensive resources to get there.

Maybe they already found a planet they want to go to, and it has more amenable climate, all the unobtainium they need, is just the right size, with just the right amount of water, and the right amount of hoomans. And much better location, you know what they say about the planet estate market.

But it's a very long haul, so they stop every now and then to recalibrate, just to be extra sure they won't end up in the middle of nowhere—where there isn't even a semi-rational civilisation like for them to run some code. How awful would that be, never getting to your new home because you didn't stop for directions and now you're lost? No sir, I'll take 20 years on Earth any day.

And as for why they don't simply stay, just think with me: if you were moving to live by the beach and made a stop in a sleazy motel along the way for a little shut-eye, would you suddenly decide to live there just because it has a pool? And what, ignore the cockroach infestation? If they do have an extra long lifetime, it becomes even more drastic. Ever stopped at a gas station for directions and just decided to live there? No? Figures.