Wow! What a great opportunity: The ability to spend a year abroad during which your family will still earn 65k or more. You can and should do it. I think you will have zero regrets, and this is not remotely a financially irresponsible or precarious situation given your massive cash on hand and the sabbatical salary.
A few thoughts.
First, the finances piece, and your angst about that. You haven't put out your approximate annual spend, but you say you live a "frugal lifestyle." Traveling abroad does not need to change that. Even if you budget 20 or 30k above your current annual spend, that would afford you a luxurious year at any of these locations (and an obscenely opulent one in Central America). You have a massive (and I mean massive) amount of cash on hand. Many families could travel the world for 3 or 4 years (or more!) on that amount of cash. You do not need to add another 30k to your cash savings to make this plan viable.
I'm honestly not sure where your angst is coming from, and I'd encourage you to think that through. Is the real worry that you will have to forgo your FIRE savings for a year?
I am also inferring that you have not travelled much before. One way to overcome your anxiety might be to embrace the fun project of learning and planning to travel affordably. And just to be clear, this doesn't have to be extreme. Airbnb instead of hotels, mid range hotels instead of fancy hotels, some periods of trekking and camping if you are into that. Consider slow or semi-slow travel (i.e. a month or even just a week in a place instead of a weekend). Target destinations slightly off the tourist trail, or on the shoulders of peak season. Use public transportation. Go to grocery stores and eat some of your meals at home. Embrace cheap street food (almost always among the most delicious meals I have traveling anyways). Bank some travel rewards from credit cards. Be flexible on flight times and destinations (this works esp. well for Europe). Do group birding tour instead of a private birding tour. Etc. etc.
Still, at the end of the day, seems like some piece of this is psychological. Others on this forum will speak to this more eloquently, but opportunities like this are what FI is all about. The $ is a means to an end: Living a fulfilling life. You have an opportunity to enjoy a great year with your SO at no risk to your financial health (that is the point of the sabbatical $!!). What is holding you back?
Second, on some of the nitty-gritty:
The medical insurance: My initial thought is, if your current insurance covers treatment in the event of relapse, be very careful of changing to a different insurance if there is any uncertainty about coverage. Is the worse case scenario something worse than you have to cut short your vacation and buy a plane ticket home? If so, that plane ticket is cheap to self-insure. In terms of other medical concerns while traveling, you can buy travel insurance for fairly cheap that will cover you for traumatic injuries and such.
Cars: You don't need to lease one abroad for a full year. Other than maybe New Zealand (not sure there) public transportation options will get you most places you need to go and as bacchi said, you can rent a car for a week here and there as needed. If I was doing this, I wouldn't sell my cars here, I'd cancel or suspend insurance and squeeze them into the garage.
Home: It doesn't sound to me like you need to rent to make this financially viable. I'd do whatever makes you most comfortable. Renting will be a hassle, but then you don't have to be anxious about "wasting" 24k or whatever on your mortgage payments.
Finally, just to give you some perspective and encouragement from my own life: Our tentative plan and goal is to downshift to a coast fire path soon. My SO has already transitioned to part-time self-employment, and I hope to leave my job in ~ a year. We have one kid. When I do that, we are planning a semi-sabbatical year, where I will have no income, but SO will still work some. We won't get to leave the country for a full year like you (too many dogs and cats we are responsible for), but we hope to take a three month trip, several one month trips, and lots of travel in the U.S. in between. Our base annual spend (accounting for a new slightly larger mortgage) is ~50k. SO will still make money that sabbatical year, possibly enough to cover all expenses. But being conservative, our goal is to bank ~35k, which would mean if SO only makes 35 or 40k, we will be fine. I'm very confident that we can have a great year within that 70k figure, there is a pretty good margin of safety built in.
The point? One, you should just be way more excited than anxious about this opportunity. Others (like me!) are planning and striving and motivated to put in place opportunities that are just a taste of the full year experience that is all T-ed up for you. Second, your financial margin of safety on this is so immense. With your cash hoard, you could do this 2x over without trying particularly hard, never mind the sabbatical salary.
Go for it!