Bidness Woes

For my business, I independently contract with a company I'll call LatKes. LatKes recently rolled out a new website. On this new site, more of my stats are available to me.
   Earlier this year I noted a significant and repeating discrepancy between ostensible income (calculated simply by multiplying [number of students] by [number of scheduled lessons] by [price per lesson]) and my real income. I make a lot less than it looks like I will. It didn't take long to figure out why: cancellations.
   I've been, therefore, aware that cancellations are eating up potential earnings (I even took it up directly with one cancel-happy student), but I didn't track them precisely.
   Enter the new LatKes site with the new stats.
   A whopping third of my scheduled lessons for this year were cancelled. That includes any students who stopped taking lessons and cancelled anything remaining, and the lessons I cancelled when my computer died in September. So it reflects more than just current students and includes my own cancellations. Even discounting those things, easily one fifth of my planned lessons fell through!

I want next year to be different. My problem is that 85% of my clients are through LatKes and I can't change my cancellation policy for them. They have the option to cancel up to 24 hours in advance.
   What's an independent contractor to do?!