I'd just like to report back that a lot of these things have helped a lot! He had a bit of a break-through on Tuesday! We did dressage practically all week and by the end he was carrying himself very well. He still needs work with his straightness, but I don't expect that to be fixed for awhile, and his right lead canter will probably just be a muscle building thing (although even in this short time, by repositioning myself, it has gotten better!). The tripping has pretty much gone away - none at all this whole week. Keeping my fingers crossed that it stays away. He still has moments where he will try to hollow his back and bring his head up, but they are much less frequent. Now (when we're working) its about 75% of the time he's carrying himself well.
I've moved my hands closer together and I have started working with shorter reins (request from my instructor). In doing so, my hand rotated so my thumbs were on top and I feel like I have a better connection with his mouth!
Just want to say thank you so much guys!
And one more thing...
We were trying to get him to collect up his step just a little bit, and I know how to ride it, but I really don't know what I'm doing in dressage yet, so I can't identify it in pictures. My instructor was there (she was teaching me how) and I could definitely feel the difference. Anyway, in the above picture, is it at least sort of what I should be looking for? And ignore me - she had me posting really tall (but staying light in the saddle) to bring my shoulders back and help me wrap my leg around him. And the picture was at an awkward time when I was shortening my reins - I have fixed my hand trust me!
Anyway, thanks a bunch!