I would do a tile rug, something that looks like an intentional design. Like how they did here under the pool table (not an island, but similar idea)

I wanted to frame my island in a mosaic pattern which would follow Beagles suggestion of a "rug" look. It would just look like your island was sitting on a carpet. You could always use a high contrast stone, for example; if your tiles are beige, use a dark stone such as Emperador marble or a dark travertine such as Nocce.

[Contemporary Bathroom design[(https://www.houzz.com/photos/contemporary-bathroom-ideas-phbr1-bp~t_712~s_2103) by Atlanta Interior Designer Joel Kelly Design

[Traditional Powder Room design[(https://www.houzz.com/photos/traditional-powder-room-ideas-phbr1-bp~t_713~s_2107) by Toronto Interior Designer BiglarKinyan Design Partnership Inc.

Good Luck.

I wonder if you could install the tile in that area using the same color grout as before. Then re-color all the grout in the kitchen including the new grout. It sounds like the old grout might need a face lift anyway and grout colorant comes in all colors.

Here is a link that might be useful: link

Thanks! I was able to search using "tile rug" for ideas. Recoloring all of the grout is an excellent idea! Thank you!