The first thing your father needs to do is to be evaluated by a transplant team, Generally they are the ones who have the ultimate say on whether or not your father is a transplant candidate. Has he been evaluated yet?
I am no expert with end stage heart failure, but one thing which comes to mind is an assist pump. Is it possible for the cardiologists to use a pump inside the heart such as a tandem heart system pump? I know this takes a huge workload off the left side of the heart, allowing the left atrium/ventricle to relax more. But, like I said, I'm not an expert and I feel for, what you are going through.
I wish I had the answers for you. Obviously your Dad is in no condition to work out at the gym to help lose weight. The most he can do is cut back on calories but that may take more time than he has to lose the weight. Not sure how much weight he has to lose.
I'm assuming he has an ICD and takes all the proper medications. Compliance is sometimes a problem. My Dad had heart failure after 4 heart attacks. He kept complaining about the various heart meds, didn't like them, didn't want to take this one or that one. His heart got so bad they told him he was in end stage heart failure and put him on hospice care.
At that point he decided to follow directions and took the Amiodarone (the one he hated) and other various meds. His heart stabilized and after the 6 months, he was off hospice care. He got another 2 years of life after that diagnosis and eventually died from lung cancer.
I don't know if there are some other meds your Dad can try that might help in his particular case. Perhaps his heart is too badly damaged. In any case, treasure every day you do have with him. Those last few months with my Dad were not easy to watch and certainly not easy for him but it was in those quiet moments that we connected the best.
Take care, irene