There's some great advice here above, and I definitely agree with most of what has been said. I would change a little bit in that letters actually can make a big impact, especially if it comes from a big name, since the cardiac anesthesiology world is pretty small and very close knit. A strong letter from a f That being said, why do you say you are having trouble getting LORs? You really don't need them for some time (late November at the earliest if I recall) and have plenty of time to work with certain attendings if you need more interaction with them. What about the people you have done research with?
As for CCM, I would proceed only if you want to. I agree with everyone else - the match process doesn't really work for having CCM as a "backup" since there are different dates (CCM a month earlier), plus if you submit a CCM rank list (and cardiac) it asks you withdraw from other matches - not doing so would lead to some consequences, including not being able to do either fellowship potentially. Do not do CCM as a method of getting into a cardiac fellowship as it would add an unneeded year and probably wouldn't help boost your application all that much. I strongly considered doing combined CCM/CT, but decided against it since it wasn't what I wanted to do with my own career. There are only a few places that formalize a combined fellowship (from what I remember - Penn, Stanford, Wash St. Louis, UF) with others offering one after the other. This is USUALLY combined with CCM because programs have had issues filling those spots, but I know several who have done cardiac first and then CCM. It's a personal decision for you, and one that I and others would be happy to discuss with you further if you'd like.