Pic of the grout crack

You will have to rebuild the entire top. Meaning demo'ing it all first. Demo of a tile counter is a very messy PIA. If you can do that DIY, you can probably get a remnant piece of a stone slab installed for just a little more than all of the materials (and time) to redo it in tile. And then you will have a smooth no grout surface on which to work.

Thanks for this. I had assumed it wasn't as easy as replacing the tiles. I would think a slab, of any desirable material, would be significantly more expensive than the tile would be. Do you have special sources for remnants? I was also considering to do the top in butcher block instead, which I may attempt to build myself.

Is the same tile on your surrounding counters? I agree that a better solution would be a solid surface top that complements the other counters. I don't know where you live, but most fabricators have remnant pieces you could select from. It would be so much better than tile and much less work to install. I would definitely look into that before starting such a labor intensive project. Plus, I think 2 different tiles in the same space would look strange.

Why not just fix the grout? If you are going to take it all apart do something solid, if not just fix it.

to give you and idea of remnant cost, at the granite fabricators here, granite ranges from $70-$110 per sq ft but the remnants are between $50-$60 per sq ft. not sure how big your island is but it may be possible to get a remnant.
also hd and lowes are cheaper that granite places in my area but i didn't want to risk a bad install with all the counters. with just the island piece (no cutouts or sink install) i would think it would be fine to go with the box stores. they have sales on counter material all the time.

Thanks for all the input! I don't like the color of the tile, so I had wanted to switch it out with something else. The hole in the grout is always covered so its not a worry of mine. Sounds like something solid is the way to go, but I think it will be a bit higher than the budget I planned for this project. Anyway, all the input is very helpful.

If you are still reading this thread.... Maybe consider very large format porcelain tiles.

check out this kitchen.

Here is a link that might be useful: porcelain tile counters