FL/GA Hunter,
Don' t be sorry. Nothing wrong with aspirations. Nothing wrong with planning, acquiring, and getting ready. " Elk or bigger every other year for the rest of my life...." you are going to be in the top 1% of USA hunters if you get onto that track --- good, I like that. Everyone is going to offer you advice, and if you bump into my posts you' ll know I lean toward the big calibers and similarly there will be plenty of folks with heart felt convictions to the contrary. Ultimately you will have to decide.
I don' t know how deep your pocket book is, I assume it is not unlimited, so I' ll take a chance and recommend the following. Use your 270 for your first trip. Go heavy for caliber on the bullets 150gr if you buy your ammunition and 160gr if you reload it. No plain jane bullets -- go for Noslers at a minimum. The reason I say pass on the new rifle is because your first trip for elk will be your most expensive (not counting possible outfitter fees) because in the two months before you go you will buy more stuff than you would imagine. Why? You' ll need to " gear up" Plus, unlike a day trip to the local deer patch, there is " too much on the line" when you do a 2 week multi thousand dollar elk hunt. While you are on the hunt in strange, new, and wonderful country and in camp with hunters equipped with a multitude of othercalibers/cartridges you will form your opinions about what you will need later AND you won' t need to rely on others for your answers. Trip #2 won' t require so many " prep" purchases -- so you can work the rifle in then, if YOU feel it is necessary.
With that said, I would point out that many hunters find a big, new, out of the ordinary hunt is as good of an excuse as any to buy a new rifle.

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In answer to your question, " ..... comfortable taking the biggest elk in the world with a 270......"
-- No, given that GOLDEN of an opportunity of encountering such a majestic animal, I could not count on the elk, in that magic 15 second window of opportunity, to present me with a " no bones" clean boiler room shot that a 270 favors -- I' d hate to have to pass on such an animal because my rifle dictated that I couldn' t take a less than favorable shot. I prefer a rifle that gives me the latitude to " nail" them from absolutely any angle offered: through the shoulders, square on, quartering raking shot-- I don' t want those limitations.
Here is a quote from Craig Boddington (more than 20 African safaris & mucho NA game) and author of " Safari Rifles" ..... " Whoever started the rumor that African game is tougher than North American game haven' t hunted elk. They are tough like Cape Buffalo are tough and if they only had the same temperment there would be little discussion over which calibers were sufficient, only the largest would be considered....." He then goes on to describe the punishment he was witnessed elk take before going down.
Okay, that is a theoretical quote by ole Craig; however, if what you are used to hunting is Georgia/Florida deer like your handle would imply, then one of the biggest favors I can do for you is to convince you that e-l-k a-r-e d-i-f-f-e-r-e-n-t! They might kind of look like deer but that is where the similarity ends.
If you are going to hunt that wide of an array of big game as you aspirations would indicate, then I put forth the logic that it makes sense to acquire a worthy set of " tools" to get the job done. It don' t take a very big tool box fortunately:
22LR for practice
223/22-250/243 for varmits
270/7mmMag/3006 for deer, antelope, etc
338 or so for the tough/big/dangerous stuff
Best Regards,
EKM