I hear Good Sams is better towing service than AAA. I've talked to both towing services pretty thoroughly. I have never used either one but when I took my last trip I went with Good Sams.
I do carry tools and spare parts with me when traveling solo.... not just solo but anytime I take a trip. You can't predict everything that may happen to where you may not carry everything that you need... and I wouldn't worry about it either. If you are not able to do the work yourself, but someone else maybe able to assist you if you have the tools and/or parts you might need if simple repair. What will happen will happen and you deal with it at that time. I am not sure if you ever wrenched on your bike before or not... I wrench on my bike but you can't fix every single problem alongside the road either. A good towing service... a cell phone to where you can call for assistance but you also may be in a location where you may not have good signal. That has happened to me once. Luckily, A good friend was with me to where I was able to use his phone to call for a tow truck that particular time of my trip. Annoy book has been successful for a lot of people and has helped my friend as well as we have helped folks who have contacted us. There are great folks out there that will be willing to help.
Enjoy the trip and I wouldn't sit there worrying about breaking down as it will only ruin your trip if you constantly think about that.
There have been lots of wonderful suggestions.
Not sure how far your LD trip is... but I would make sure you do a maint such as tires, oil change, and other necessary checks to make sure there isn't anything wrong with the bike before venturing out on your LD trip.