When I first started Jujitsu,I did not understand what the purpose of all the rolls was. We rolled and rolled and rolled. Front, back, left, right and combos of all the above. Later the instructor showed the combat applications of the rolls and the breakfalls. Where ever your body is falling, there is a roll just waiting. All the other systems I have studied since, all have the basic rolls.
I say rolls rather then breakfalls becouse a breakfall you stop your momentum when you land. The roll you can contact the ground and keep going untill you roll back up. Even from the kneeling position you can roll and mantain a kneeling or low position. Nin-po practitioners are some rolling sons of guns, Man can they roll.
So the answer to your question is to try to roll when you fall. Whether its a forced push down or take down, or you throw yourself into the rolls. Start out on grass or mats. Then when you get good technique, try it on concrete or asphalt or gravel.
I do Airconditioning and heating on commercial buildings. Most of the units are on rooftops. I'm always tripping over the gas lines that feed the units. They install them right at shin level. The rolls have realy saved my butt. A lot of people in my department have broken there wrists or landed on there faces,
becouse they did not know how to roll. With your Muay Thai back ground, you can learn to roll back up straight into a kick or elbow strike. By the way every thing you do standing up, you can do on the ground. Try rolling into a kneeling position, from standing and then fire some strikes and kicks. Then roll any direction to a standing position. Then do combos. of rolls kicks and strikes. Rolls are great. My Arnis instructor always had us rolling around into different positions with sticks and knives. You even learn to jump into a diving roll to pick up weapons. Did I mention That rolls are great. I'm sure others will have different techniques to get you back on your feet that are equaly as good. But for me, its the rolls.
Your freind in the Combat Arts, Redfive