Wanted to give a huge thanks for everyone contributing to this post and to
@paflytyer for the great step by step guide. A few notes from my experience (these may be very obvious and specific, but for a noob like me they may be helpful):
1. Soapy water is KEY and is very helpful in getting those clamps to move
2. First just worry about turning the clamps for easier access, don't try to actually move them off of the T's in their original orientation
3. Patience, patience, patience...it's so easy to get frustrated with these things. I would move one clamp, take a beer break, move the next clamp, beer break, etc.
4. Work from the passenger's side also. A couple of the clamps on the T closer to the passenger's side were easier to get to from here (sure you're pretty much laying in the engine bay, but it works)
5. I used a cup to catch the coolant as the OP suggested and this worked really well. The first hose that I pulled off was from the forward most part of the driver's side T. When that came off, coolant started to leak out of the exposed end of the T, and a small plastic cup was perfect to catch this and top off the coolant when all was said and done. As OP mentioned, I got approximately a cup of coolant. This also keeps you from cleaning up any mess.
6. I pulled the driver's side T first as it was easier to access. BEFORE putting in the new T, go ahead and get the other old T out. Without that T blocking the way, the clamps on the T closer to the passenger's side are easier to get to.
7. Confirmed - the shorter the handles on your pliers, the better.
8. For God's sake when you install the new T's orient the clamps so that they're more easily accessible for the next person (hopefully yourself) to do this. This would cut the time of this job in half, at least.
Here are what my T's looked like after 162,xxx miles:
I couldn't break either T with my hand, but as you can see the ring broke off on one end of each T during removal. I didn't notice until installing the new T's, but these rings had become embedded in the hose preventing the new T's from going all the way in. I used a small flathead to pry the pieces out of the hoses, careful not to let them fall down the hose.
Thanks again to everyone here for the help!