If they went that route, I like the second option better. Labs produce a very small amount of knowledge no matter where they are. Say, ten labs altogether would produce 1/sec knowledge, so one lab by itself would produce a single point every ten seconds. Advanced and higher Mk labs would do a bit better, maybe a bonus for "collaboration and peer review"
if they are at the same planet. That way, you in effect are paying for knowledge because labs cost energy and energy costs resources. You just can't get at it all at once just because you are flush with raw ore---that really doesn't make any sense. Knowledge is acquired through slow research and theory in the real world, and discovery of knew things. Discovery is addressed in the existing model, it's the slow residual expansion of knowledge by scientists that isn't. Just what are those scientists on the lab ships doing whenever they are not in a new zone? Perhaps it would be better to not ask.
To keep it balanced, there would probably need to be an effective cap based on total knowledge gathered. The more you know, the more difficult it is to learn new things because new things are orders of magnitude more complex. To simulate that, and provide a limit on people just letting their labs rack up knowledge for hours, the more you accumulate the lower the percentage gets. At the beginning of the game, this produces a decent amount of new knowledge for no effort. A couple of labs would produce ~720 knowledge per hour on top of whatever other acquisitions were made in that time. In the mid-end game the player might have dozens of labs from captured and higher mark models, so while the return would be lower, the overall cumulative impact would be about the same, which keeps the game interesting by reducing management, while somewhat mirroring how science works. Things get more complicated, so you throw more resources at it.
Those numbers would probably need to be tweaked, I'm just throwing them out there to explain the concept. 360/lab-hour might not be enough of an impact. Perhaps the percentage per second could be 25% instead of 10%. That would be 900/lab-hour, or with a couple of labs close to the acquisition of a new planet every hour, with the rate of return slowly decreasing. Throw more labs at the problem, and there you are spending more effective resources to do so. This is where having a collaboration bonus could help balance things out. That way in the start of the game when you can only afford a few labs, you aren't raking it in at high percentages, but later on when the rate of return is stressed, you can benefit from having 15 labs on a planet all working together. Perhaps it could even be proximity based, like cloak boosting. Or perhaps only Mark II's or even Advanced Labs are the only ones that produce this proximity boost in a manner similar to capital ships, boosting the labs around them---that would even be a better early-game abuse limiter, and would make Mk IIs more enticing to purchase.
There are probably some edge cases where things get whacky. What if there is a Zenith power plant right next door to the starting planet. The user could deploy a huge spread of labs early off and end up getting a ridiculous amount of knowledge for free (resource usage is effectively nil)---but then again the Zenith plant is inherently destabilising anyway. If you choose to use the surplus for knowledge instead of military power, that's your choice. The only area where it would be less balanced is that knowledge can in turn be used to create a more powerful military. Once you get the huge surplus you can wipe out the lab fleet and proceed as if you had used cheat codes.