Best way to book a last-minute Shinkansen seat?

I really need super fast help figuring out how to book Shinkansen from Osaka to Kyoto TOMORROW. I didn't plan this trip in advance as my travel plans changed (sparing you the long story). What app or service can I use to do this with the least hassle (and as you can tell, I don't have much time! Your help is much appreciated!)

EDIT: Thanks everyone for the insanely helpful tips and discussion, I really appreciate it. Someone suggested this Osaka-Kyoto travel guide which lists all the options, including buses. I checked the pricing and travel time and the best option in the end was to book a Kansai JR Pass for $19!