I would give my left.....uh.....appendage...for a tune! 321GO, you will not be sorry.
When I changed the stat on my MKS, I had a small container under the stat housing and kept gently pulling the housing away from the engine until the cup was filled. I would then dump the cup in a larger container. I kept doing that until I could completely remove the housing from the engine. At that point, I knew exactly how much coolant I had lost and virtually none went on the floor or all over the engine.
After replacing the stat, I jacked up the passenger side of the car so the degas bottle was higher, added the same amount of coolant that I had lost to the degas bottle and started the engine. Let it warm up, rev and hold to 2500 RPM for a few seconds, then let idle a few seconds. Do that a few times and the extra coolant added to the degas bottle will get sucked into the engine. As others have said, keep an eye on it for a few days.