So how soon after I add the protection plan do you guys think I should call them?
If it was my system, I'd take a different approach.
I'd call DIRECTV and use the automated system to ask for tech support. I would then tell them that my signal levels are fluctuating and go through whatever troubleshooting hoops that they make you go through. Since I am not 100% certain, from what you have said, that the problem is a line of sight issue, I wouldn't even mention anything about trees. If you do this, there is a very good chance that they will set up a truck roll for you at no cost even without the protection plan. They have done so for me, and, if your account is in good standing, chances are very good that they will do so for you.
On the other hand, the approach that you are currently considering doesn't seem to me to be the best. You are considering signing up for the protection plan and committing yourself to one year of the protection plan and at least $84 in protection plan charges to avoid a service call that might well be free but that, at worst, is going to cost you $49. And, while you are delaying in calling them, you are continuing to add days when you are not getting the full benefit of the programming for which you are paying.
Also, if you want to make a rough check on your own to confirm whether or not line of sight is the problem, take a yardstick to the dish. Place one end of the yardstick at the base of the dish where the LNB arm is attached, and rest the other end of the yardstick on top of the array of LNBs. This will not give a perfect indication of your pointing, but it will give a rough approximation. As you look toward the direction that the top of the yardstick is pointing and if there are no obstructions in the arc between 99 and 103 degrees, it is unlikely that pointing is your issue.