Keepin it Wheel
Join Date: Aug 2011
Location: San Diego
Bikes: Surly CrossCheck, Moto Fantom29 ProSL hardtail
I have a tire bead jack by Kool-Stop, that's also helpful, and fairly small and light. It would be tough to fit in an underseat bag, but if you have panniers or trunk bag, you could carry it all the time.
However, might it also be an issue of practice? I couldn't tell from OP, was this your first flat repair ever, or just your first since getting these tires?
There are tips to make it easier to get tight tires on, like squeeze all the way around to make sure bead is lying in the lower center recess of the rim, start your second bead opposite the valve and end at the valve (if you start at the valve, the valve prevents the bead from sitting right at the bottom). Some people recommend a swipe with talc, maybe you could keep a little baggie of it with you?