I highly agree with the strength training responses. I'll also add here that strength training (squats, overhead press, pull ups, etc.) also works out your core a lot, since you need to engage your core to stabilize your body during many of the exercises.

You also mention that you run 8k every morning and do burpees afterward. I think you should read [this post](http://www.marksdailyapple.com/case-against-cardio/) by [Mark Sisson](http://marksdailyapple.com) about why doing too much cardio could actually be **bad** for you.

One other extremely important thing is your diet. I know you mentioned that you eat well, but recently, I've discovered that the typical person's perception of "eating well" may not actually be as healthy as he or she thinks it is. In particular, you might be consuming too many carbs to fuel your cardio. See [this thread](https://fitness.stackexchange.com/questions/4609/what-books-sites-journals-and-research-can-you-recommend-for-nutrition) for more detailed information about nutrition (I've posted a response there listing what I think is good "further reading" material). 

EDIT: Just saw your update about your diet. I'm currently following a primal/paleo lifestyle where grains and lentils are not eaten because of their antinutrients and insulin-raising (respectively) effects on the body, which could be part of the answer to your question as well. However, since your vegan, I'm not really sure what other food choices there are.

My suggestion is: try the strength training first. If that doesn't solve your problem, you may want to think about changing your diet in some way.