A majority of the Americans that I ran into that went through the "backdoor" in to Cuba go via Cancun due to price. Panama on Copa might also be an idea.
Cuba does do a visa on arrival for Americans, although you can get them in advance from the Cuban interests section if you want the security. Cuba does not stamp your passport.
I have said this in other threads, but when I was there in January, my group met with US Interest Section officials and they reminded us that even if you enter Cuba illegally, you can still use their (limited) services in the case of emergencies. They do not enforce Office of Foreign Asset Control sanctions.