In 1990, when my Gwyn four months old, one of her earliest vets heard a heart murmur. In 2002, Gwyn had what we eventually decided was a stroke. (We consulted every specialist and ran every test suggested by the neurologist -- well, excluding the exploratory brain surgery -- but heart problems / blood clots were never suggested, so there was no heart-specific work-up at the time.) She had another presumed stroke in 2006; again we ran a whole bunch of tests, but again nothing heart-specific.
Labor Day weekend 2007, at age 17-1/2, Gwyn had a third stroke; this time the clot left her hind legs paralysed for two months (she did recover and ended up walking normally). During the battery of specialists / tests during this period, we finally saw a cardiologist, who ran an echocardiogram on my Gwyn (an ultrasound specifically aimed at the heart). Among various other other heart problems, Gwyn was diagnosed with moderate geriatric-onset hypertrophic cardiomyopathy.
The cardiologist we saw was board-certified and, from our research, was one of the best in the area. He's also inclined to be conservative with medications. He said that we could start Gwyn on heart medications (atenolol or diltiazem), but his inclination was that we should wait on that. Since he was the best we could find in the area, we agreed to hold off on those meds, although we did start treating Gwyn for hypertension. Currently, she's on a daily dose of norvasc, and she gets 1/4 of a baby aspirin twice a week.
Gwyn has never had congestive heart failure. As with many older cats, Gwyn does have lower kidney function and, like many kidney-impaired cats on this board, she gets subcutaneous fluids. However, because of Gwyn's heart conditions, we are very conservative in the amount and frequency of the fluids that we give. We also try to avoid excessive amounts of salt in her diet. That was two and a half years ago; in just under a month, Gwyn will turn 20 years old.
As for your cat: there are different types of HCM -- I seem to recall the cardiologist saying there were three main types? -- and there are different severities. You'll probably get folks with different types and different severities, and I'm sure there are differences in how each one is treated.
Before you make any decisions on Ginger's future, I'd suggest seeing a cardiologist, preferably a board-certified one. They'll probably run some tests, and will hopefully be able to give you a more knowledgable diagnosis and treatment plan than your regular vet. Which isn't to diss your normal vet, I'm just saying that there's a difference between someone who treats a range of problems in a variety of animals and someone who's only job is to look at hearts.
If you do see a cardiologist, make sure to get a copy of the report for you to keep yourself, so that you can refer to it as needed and can provide copies of it to any other vets you may see in the future. For example, given all of Gwyn's heart problems, she's at a high risk for complications if she ever has to undergo general anesthesia; the cardiology report gives an entire list of things to do before, during and after the anesthesia to keep those risks to an absolute minimum. It also discusses drug possibilities, diet, activity, subcutaneous fluids, etc.