I have an enlarged heart too, cardiomyopathy with congestive heart failure. My ejection fraction is now at 30%, used to be at 20% and they sent me to see about a heart transplant a few years back. I will eventually need one but for now they are trying to get all they can out of my own heart. My arteries are clear and my heart failure was caused by a virus attacking my heart. Not typical heart disease at all. My blood pressure is actually on the low side, always was and I was diagnosed at age 30, I am 34 now.
Whew, I was worried this diet would be bad for my heart too. I weighed the risks against the fact that at my current weight I would not be eligible for a transplant. I need to get down to 180 to be considered or else they will pass me up.
I have been searching for info on heart failure and atkins lately and I haven't found a lot of info but I suggest you check out this site:
www.jonsplace.org
I am still researching the effects of this diet on heart failure and I will post here if I find more info because this is really important to me too.
I can tell you that my cardiologist has told me that getting the weight off is the single most important thing I can do to get my heart back to normal size and functioning.
Some variations I have to make to atkins (low carb) dieting to fit my health condition:
Restrict fluids because of the risk of pulmunary edema.
Keep the sodium level very low.
No exercise as I am not allowed to strain my heart.
Now, with these adjustments I know I am going to lose weight slower than someone without my disease plus I am on a lot of meds which are probably slowing me down as well. I have to accept my weight loss will be slower but that's ok. I don't want to end up on machines and the doc tells my family I am too fat for a transplant. Simply put...he said there are not a lot of hearts to go around and they can't waste one on someone who is overweight.
Please let me know how your aunt is doing and in the meantime I will be searching for some info.
Take care.

~Cindy