After a lot of consideration and looking at the quickly dwindling house budget (flooring is like the most expensive thing ever!) we have hesitantly decided that painting the brick is the best way to deal with it. I think that we have come to the conclusion that some day we would like to tile the whole fireplace. Alas, we both have very expensive taste in tile and with close to 200 sq/ft to tile, we just can't do it (now).
Jarrod stopped and picked up a few paint samples and did a test on the brick. From a few feet away it is quite convincing! The mortar in the rest of the house is far more pink, so it will take some tweaking to get it to match, but I think that this will be a reasonable alternative in the short-medium term.