Nice, Muay Thai is a great way to make your body a hell of a lot stronger, it transformed me. All the plyometric stuff is really good for your back.
Good luck with it all, avoid those thais when it comes to clinch.., otherwise you will spend a lot of time being chucked on the floor!
The core is the key, it is your foundation/balance etc. Weak core weak body. I learnt from watching a DVD of the 2009 Lions tour to South Africa, the strength & conditioning coach was a free style wrestler. He was alot smaller than many of the Rugby players but threw them around, he explained the core is the key! Things like the plank are great, clap press ups strengthen your back, yoga stretches are great as well. I do them everyday in front of the TV, you don"t have to go to a gym, do them in your front room..