The short version: He has definitely had some extensive desensitization training, however he is also very curious of anything new. We've thrown tarps on him, thrown the whip all over/next to him, and even accidentally thrown a ball at his head with not a reaction. The only thing he seems to be afraid of is the indoor in bad weather.
The saddle is not a great fit, I'm going to mess around with it (it is a Wintec) and change us the gullet/riser system. If that doesn't work I'm going to try some other saddles.
We have been doing tons and tons of lunge work/other ground work, and Parker has generally been very good with it. Every so often he'll get hyper and throw a little bit of a hissy fit, but he is starting to shape up and feel his oats so it is too be expected.