I'd replace it. Check to see if the floor carries beneath it first, otherwise you might be forced to match its shape with your new island. Kitchen islands have become the central entertainment areas in homes to serve snacks and seat guests. You'll lose some storage space, but gain on function.

I agree but if the rest makes sense then changing the island to rectangle all one level is what I would do but IMO the whole space needs a revamp

Is there a stair way behind the desk thing?

Wow, that kitchen is a hot mess. Lose some of those angles and some of the ups and downs. Makes my eyes flutter!

I would take the desk area out. That alone will help! Island should be square or rectangle, depending how much space you have. I'm sure you're constantly asking yourself "where do I start"? Good luck. Post an after... I'm sure it will be gorgeous!!!!

Yikes! You do need a kitchen/space designer. This is not an easy cosmetic fix. Although your space looks highly functional and in great shape and with plenty of storage, there is no way to drag this thing forward. If you just redo the island, you will end up having to redo the floors and you will still have a weird dated kitchen. Tile tops are the least of your problems here. Sorry, but I'd either live with it or start over. Living through a gut remodel in the middle of your living space is going to be nearly impossible with your layout too. Good luck!

Given the willy nilly, nervous aspect of it, I'd do some serious shopping around but my first cal might be an architect to consult/brainstorm on smoothing the footprint itself. THEN with an improved footprint . I'd sit down and put some idea books together on Houzz that represent the flavor you'd like for the kitchen . A great result is far more than changing out island and tops here. Someone who asks "what do you want" in this kitchen, is not a designer, they are a cabinet salesperson.