This is a loaded question.
In business strategy, one of the things that's done during the planning phase for changing a business's strategic direction in an existing market is something called a "swot" analysis. It's where a company analyzes its strengths, weakenesses, opportunities, and threats. As a fighter, creating a strategy should be no different. You need to know all those same factors in order to create a successful plan of action.
Strengths:
What I can gather from your post is that you have a inclination towards punches. I assume by that you mean that you have a set of mechanically sound punches. What are your other strengths? Are you good at blocking/covering? Do you have KO power? Are you exceptionally fast?
Weaknesses:
Being good at punching/boxing/fighting with your hands, means you'd have the footwork to go along with it and that translates to being able to control the space and positioning as well as the timing to know when to punch. Your quoted statement above implies otherwise. So I would say that might just be your set of weaknesses.
Opportunities:
You have several opportunities in your strategic direction. You can increase your knowledge of Muay Thai to learn how to take advantage of the typical nak muay's plan of attack and learn about holes in their defense. You can increase your fighting attributes to become stronger, faster, more reactive, or more resilient to punishment. You can learn to kick better so that you're stronger in that range of fighting. Lot's of options...
Threats
In the context of fighting...fighting a muay thai fighter is complicated. You have 8 limbs to deal with, and so many different varieties and combinations of attacks that it would be impossible to know them all. The gatekeeper for a nak muay are their kicks, as you have experienced. Those come at all elevations, but typically from ground up angle if it's their version of the round kick, or they may come straight forward from roughly waist level. They might come from a high angle downwards, or from a spinning maneuver at your side.
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Based on this rough SWOT analysis, I would say that your best plan of action would be to learn more about Muay Thai's general offensive strategy and counter attacking methods. Make note of how a typical nak muay would move, and then create some tactics to circumvent those standard reactions to allow a higher probability for your attacks to land. Combine that with learning better footwork and timing, and you likely will have a good recipe for success.
But, that's just my assumed analysis. You know yourself better than any of us do. Using this format of thought process...what answers would you come up with?