I hate to say it but you have little chance of passing the FAA medical. The only way would be if they grant you a waiver and given the nature of your health issue you would have little chance. I talked to my flight surgeon friend and he agrees. He said maybe around a 10% chance. You can, however, get a LSA without a medical. The kicker here is that if you go for the medical and are failed, the LSA is off the table. So, if you want to pursue a LSA, don't try to pass the medical for Private first. In any event, I wish you the best in your pursuit.
If you have a valid driving license you gan get your sport pilot license, there is many kind of Special Light Sport Aircraft and Ultralights planes. To get this license is pretty cheap, fast and easy, only 20 hours are the minimum requirement and usually the hours ae cheaper than Private license.
Unfortunately, I am living this nightmare as we speak. I had a heart attack caused by a blood clot from my leg requiring a stent to be installed. With that comes the nightmare of trying to keep my Medical.
I have a great Doc who is working with me very closely. Fortunately for me, the damage to my heart was not too bad so the recovery has been going good. Once i get released from my cardio Doc, then we will see if the MRB will even accept a Petition for reinstatement. If they wont, I guess I'll be a Light Sport Pilot.