There are at least 3 money changers on the main street in Chetumal. The last time I went through, their rates were the same (maybe a little bit better) as the rate at the border.
I've also changed at money changers in Playa, but the rate wasn't as good as Chetumal.
I've tried to exchange cash at banks in Chetumal without success; they told me to go the money changers.
ScotiaBank operates in both Belize and Mexico. If it's a large amount, you might consider opening accounts in both countries and doing a transfer. There might be fees, but worth checking out.
Edit to add...
My comments refer to changing BZ$ to pesos.