I'm not sure what your travel plans in Mexico are, but:
What if you traveled overland down to Guatemala from Mexico City, and then came back up to Cancun, maybe even stopping off in Belize? Or, if you are just interested in the Caribbean, traveled to Cancun from Mexico City, went down to Guatemala, and then came back to Cancun? If you were interested in flying any of these routes, that might be doable last-minute, but of course using the bus system would still be cheaper and more flexible. BTW, the first-class and business-class buses in Mexico are ridiculously nice and luxurious.
If you do that, now you know you can get from Cancun to Havana relatively easily, so that's covered, though you may want to check and see if you'll need a return/onward ticket in order to get into Cuba.
Now, you know you can get to Jamaica from Cuba, so now you just need to sort out your trip back to Mexico, which I guess is still you're biggest headache. It looks like a r/t Cancun-Havana with a r/t Havana-Kingston in the middle of it may be the best way forward.