The person to ask about pricing more hardwood and installing it is your hardwood flooring professional. Ask them what his labour/material costs would look like if he laced in new hardwood into the kitchen and then sanded/refinished everything at once.

So long as you can find the same plank width, cut and species (very important) it is very possible this can be done for less than you think. These narrow planks are relatively cheap because they are not in fashion. Sourcing them may take a bit of time (especially if they need to be milled for you) but other than that, it isn't a huge impact on the budget. It should be less than a tile floor.

Sure....tile. Or sheet vinyl that looks like stone, or tile.