This is one of the rare occasions where you have a very strong negotiating position. Use it wisely: The best approach here is "situational". Take your cues from their reaction and responses and adjust as needed
Step 1: Start with a neutral resignation later. Keep it short and simple: just that you resign and your effective departure date. If you get no reaction or just a cookie cutter response, than you are done. It means they are perfectly okay with you leaving and you should take the hint and go.
Step 2: If someone asks "why are you leaving?", you need to gauge who is asking and why. Only talk to someone who can make a material change: you tell them your story truthfully an accurately: "Too much travel and all attempts to reel this in have failed". Make sure you have some examples of what you have tried, so they can't weasel out with "I didn't know this". Don't say anything more, and wait what they do.
Step 3: If they want to keep you, you want them to say "What can we do to keep you here?" or "What needs to happen so you would stay?". If you are not getting this, it's probably not worth staying, since they are not interested enough in you. If you get the question, carefully state the goals but try to push as much of the details and specifics on the employer. "I really need my travel to be no more than 1 week/quarter and I don't see a viable way to get there. What would you suggest?".
Step 4: negotiate the details and make sure there are hard deliverable or concession. When they make a suggestion, make sure it is specific and detailed, can be clearly documented in writing and it contains a clause that describes the consequences when violated. Just them saying "ok, we'll have you travel less" is not sufficient. Be firm: "I need something in writing or an amendment to my contract that clearly limits the amount of business travel". If they suggest something that they have tried before, just say "we tried this before and it didn't help. How can I be sure it would be different this time?". At the end of the day, they need to convince you that they have a credible path forward, and it's your decision what "credible" means.