Personally I would go for a feature strip / threshold piece between the two areas by cutting out the rest of the tiles to make one long strip wall to wall.
Then speak to local marble fabricators one of which will hopefully have an offcut of 20mm Travertine slab that could do the job. Only issue could be thickness so they may have to round both long edges, or grind the back of the slab and split the strip into 3 - 4 pieces so it can be fitted flush.
You will never find a perfect match to the existing tiles so better go for a darker contrasting travertine like noce.
if you try and find a close matching travertine, replace some tiles and then grind and repolish the entire stone floor you will still be able to tell the difference between the new tiles and orignals.