There are decent cheap tires out there. A number of owners have had good luck with the Achilles ATR Sports. $75 for fronts each and $105 for rears each approx.
You can find a number of cheaper tires here:

tires online @ tires-easy.com: tire dealer for cheap passenger, summer, winter tires

 

I put on Cooper Xeon RS-3 S's last year somewhere around $800. The Toyo Proxess T1R's I had on before that were closer to $1,200. (Not all makers have those sizes standard on the XF. ) This was from Kaufmann Tires, a FL chain, if you mail order, I'm sure you can find some for less, but with shipping and mounting, still probably would be close to $800 min. If you go more exotic and semi-race type, I think you could get close to $2,000 for a set.

I would NOT change the size of the tires, if it was me.