i have done a couple of this type of conversion 27" to 26x2.0 and have cleared the frame both times. The 2.0 tire fills the frame nicely but side/center pull brakes may not work. Older 10 speed bikes and BMX sometimes have longer brake arms that you might be able to get to work or old huffy MTB bikes have a horse shoe looking adapter plate that will let you run cantilevers with out welding studs to the frame, you could also add a rear disk to it.
Troy