Hi! I'm pretty new to the game, with just over 300hrs of experience in it. I've not had this problem before, because I generally stick to low numbers of Kerbals in my ships.
I think you're probably right in saying that the problem is caused by the rendering of the individual Kerbals, and I'm not too sure if KSP renders them in the background. If you've not already, I would try minimising the view of the Kerbals and seeing if that works. KSP might still render them in the background, but I don't have anything else to suggest, sorry.
If all else fails, you could try your ascent into orbit via the map screen. I do this sometimes with bigger vessels, doing the gravity turn using KER readouts (or you could use the stock ones from the ship info on the right). This significantly improves the game's performance for me.
Anyway, hope I've fixed the problem!