I would never go on a big trip without a backup body. But I feel a camera like the A7III is good enough. I would not tie up $4K on a camera that probably won't be used.
Having owned a 300 2.8, I would not own that lens except for sports and certain events.
It's such a personal call, because it is a lot of money to shell out on a prime. It's a truly exceptional performer compared to any like lens that's come before it, it retains a lot of its greatness with either extender, and it shaves about 800g off the last DSLR lenses of this type. I love it because I do a lot of shooting with the bare lens from the back of medium sized auditoriums and theaters and I'll use it for outdoor portraits and dog shoots. When I'm hiking with it, it's typically got one of the extenders on it (most often the 2x) and I barely notice the additional weight. I also do some landscape with it, and it is so rewarding when the focal length is right for the shot. It's not my most used lens, but my appreciation for it is sky-high when I get the opportunity to put it to use.
I doubt any of that tells you if a fast 300 is what you want or need. If you can, I'd suggest renting it and the extenders for a week when you've got some time to dedicate to it. Using it in the situations where you'd otherwise rely on the zoom should tell you if you'll have a hard time with switching lenses when you need the wide end and/or how much of a hassle it will be to use the extenders when you want more reach. I know it's an expensive rental and there's an argument to be made for buying used and selling with little to no loss, but there are risks to that, and it will take time and effort. Renting (with insurance) is a no-risk and minimal effort proposition, and you'll get all your questions answered by your most trusted source.
