I don't have the cough but my reflux is pretty severe. Initially I thought I had ulcers or a gallbladder problem. I could barely eat for months without causing stomach upset/ stomach pain. I lost a lot of weight. And yes I'd frequently wake up choking on acid refluxing into my mouth. Nexium makes a big difference, but even on it, I can still wake up choking on reflux in the middle of the night - only the fluid doesn't burn because the Nexium has neutralized the acid. I have also had referred GERD pain that made me think I was having a heart attack.
On occasion I'll get hoarseness and sometimes a cough, but it's not chronic and usually goes away, particularly if I up my dose of Nexium.
Diet has never made any difference, though alcohol (more than 1-2 glasses of wine) definitely does not help, and having a heavy meal right before bedtime doesn't help either.
Sometimes I can successfully taper down my dose and even go off of Nexium for awhile, but it always comes back eventually. Sometimes (lately) I've noticed it's getting worse even while on what should be a perfectly adequate dose. You have to taper Nexium or else you experience rebound ? which can be pretty severe. I am a champ at the long slow taper now. But even then, it seems to always eventually come back, for no reason I can pinpoint - not diet, not alcohol, not eating too close to bedtime, etc.
There's all this stuff on the web about how some with GERD have low acid, not high. And there are sites that recommend a way you can test this, with HCL challenge. I tried that once and even with just a single pill or two, had severe stomach burning. So I am confident my problem is not low acid. With silent reflux, that may be case I suppose - did your doctor mention that?