The point is we don't know how hard the LSAT is / how good your study habits are. You CAN suck it up and study for two tests at one time...but only you know if that is a good idea.
Here are the circumstances that I put together my package under:
Last semester I was taking the following courses:
Intermediate E&M, Optics, Communications in Physics (yay easy), Partial Differential Equations, and Quantum Mechanics A
I was also working 25 hours a week at a national lab, studying for the physics GRE, and prepping to take the ASTB, which I think I ended up taking one week before finals week.
It turned out to be a little too much for me to handle: got straight As, got a 8/7/8 - 69 on the ASTB, but didn't too so hot on the physics GRE.
The point is you make a decision and take your chances. It is absolutely in your best interest to apply as soon as you can put in a good package. If Law school is your number 1 priority, then based on your posts, I would say study hard core for the LSAT, maybe take a week off afterward, and then start busting your butt on the ASTB sections you didn't do well on.
As far as timelines go, figure out when you're taking the LSAT, and schedule the ASTB for 3 weeks afterward, or however long you think you'll need to study for it. Once again, only you know how long that is.
Also, a lot of these guys bust their a$$ in the fleet. It isn't so much that they don't think your life is hard as it is that they don't think it is harder than anyone else's.