Couple of things:
I'm not sure what color smoke silicone produces; I answered without thinking but remembered that regular glycol-based BF does produce white smoke (as does anti-freeze if it gets in the combustion chamber). So, anyone burned any silicone BF to see what it does?
I overhauled a Girling servo once thinking it was the cause of some problems--pedal required a couple pumps to activate brakes--but found out later it was a damaged 'foot valve' in the MC. I had a plastic, inline check valve installed by a DPO; but sourced a working, used one from BCS, and removed the plastic one (it worked, but looked, well, wrong). The original valve was inop; they are just a reed valve--a little flapper that can only move one way--and its flap was gone.
AFAIK, most of the info in the article is correct, but I take exception to some of the wording (yes, I'm as pedantic as I am scientific). The check valve is not 'designed to suck out air that is trapped in the brake booster without letting additional air enter the cylinder.' The valve is passive; it allows manifold vacuum to vacate the air in the large canister but does not admit air at atmospheric pressure. And, when the valve has failed, it does not allow 'excess pressure inside the master cylinder, which the check valve is designed to regulate.' The check valve doesn't 'regulate' anything, else it would be called a 'vacuum regulator.' As the article does state, finally, the valve is there to allow one or two applications of boosted brakes when the engine quits (and there is no more manifold vacuum to create 'boost').
I do think Patrick's problem is in the servo, but it's not caused by the check valve, because he has lost boost even when he has plenty of vacuum. The only check valve failure that would cause this is if the valve somehow got blocked or became 'reverse biased;' i.e. it allowed atmospheric pressure in, but not vacuum, or if the valve has developed a leak, allowing atmospheric air in all the time (my dad's '65 Mustang had the describe problem, but it was because an elbow that connected the vacuum hose to the servo had cracked). The reed valve could stick open, or come apart like mine did, but the only symptom would be you wouldn't get the 'extra' boosted braking when you turn the engine off.
I think something is stuck inside the servo. Have you tried whacking it yet?
Edit/add: To confirm the check valve isn't the problem, just bypass the valve (but don't rely on an emergency boosted brake application if your engine quits). If the problem persists, it's not the check valve.