You are micro-managing the hell out of this plant. Why did you wash the roots and dust them with rooting hormone? When does this happen in nature? The mere fact that the plant is still alive shows it is EXCEPTIONALLY strong. Don't worry about the roots till next year and DON'T rinse the dirt off the roots again. It is unnecessary, potentially damaging, and frankly, more than a bit bizarre. Let the seedling grow, if you don't want it to branch you can snip off that sucker, but see if you can find a photo or actual Key Lime Tree and see if it is more single or multi trunked. I believe a sprawling, multi-stemmed form might be more in the nature of a plant evolved to survive on an island where winds can blow to hurricane force. That's just a hunch. If you want fruit on your potted tree, it will happen sooner if your plant is a bit root bound, The oldest smallest leaf will likely yellow and fall off first. As for growing too fast, each seedling is a roll of the dice in the innate characteristics department. So how fast is too fast? Just admire is your best tack, I think.
you don't mess with it until it is much larger. You worry too much. All you do is to make sure it is water sufficiently that it doesn't dry out and give it occasionally some fertilizer and once a year in spring you can put it into a larger pot.
Just plant it and let the plant do whatever it needs to do. I grow tangerines and there is nothing easier: just walk outside, spit the seeds in the flower beds, and presto: citrus!
