Surprising not to see anyone mention the tackle. It may not be permitted in the dojo but on the streets, well, there you have it.
Close the gap. Work the clinch if you arent allowed to fully grapple.
Work the jab. A lot. Keep him defensive. If he is worried about the constant flurry of punches coming at his face then he will be less likely to attack.
Once you have him pressed keep on him. If your advancing on him and then you step back to retreat he is about to hit you.
Front kick his hip. A lot of Muay Thai guys, not all, but alot of them come from way out to do this kick. If you have a front kick thats fast then kick the top of his hip bone. The force of his swing and your push is going to hurt. And it'll stop the kick.
Trying to absorb or check the attack is the last option. Simply because you are still taking impact. Impact that eventually can lead to injury.