Buy slicks for the MTB.
Maybe a rigid fork, a grand or more is a lot to spend simply for 15 mile rides.
I mostly agree, I have riden up to 70 mile on my £330 fixed wheel bike. I ride 20-25 miles often without a second thought. So you dont need to spend anywhere close to £1200 to get a bike that will do those milages, and to do them fast.
BUT......... having a nice bike can be a great motivator for actually getting out on it (or it can go the other way and you may be scared to ride it incase you damage it, being inexperienced, I had this effect with my roadie, only just starting to get past that now).
I guess the OP is the best judge for his budget. Just bear in mind if you buy a high end bike you wont be getting pedals, shoes, lights, a helmet should you choose to wear one etc etc, you will need to buy them, so leave room in your budget for this. I am aware sometimes you get say £100 of accessories thrown in with a bike, but not always so just dont shoot to high then end up with no money to actually get it on the road.