I find the Motion Pro compound tire iron works very well, not because it is so long but because it is curved and reaches around and under the tire bead easily. It is the long one shown here: http://www.motionpro.com/motorcycle/partno/08-0049
When the old tire resists leaving the rim, take a utility knife and slice it off. Just be careful not to mar the rim or your paws.
Isn't there a steel wire or cable of some sort in the bead?
The back tire wasn't any problem, except getting seated. After about 1/2hr. it magically seated and took her for a quick test spin. Thank goodness I knew enough to crawl till I was sure things were good to go, because when I stepped on the rear brake, it wasn't there.