A couple random things first:
L/Dmax = A given AOA based on airfoil. (I suspect this is what oldveedubs was getting at)
L/Dmax changes with weight based on: sqrt(Weight_actual/Weight_maxGross) * BestGlide_maxGross
Simple formula: [(Weight_change/Weight_gross) * 100] / 2
(L/D)max will only produce best glide in no-wind conditions.
This is certainly true. However, I have yet to read any mathematical proof as to the pilot "rules of thumb" being accurate. That is, increasing by 1/2 the headwind. I doubt it is linear, as the rule of thumb suggests.
I am more comfortable agreeing with the decrease in airspeed for a tailwind, but again only to a point. That point is clearly defined as min sink or minimum power required.
FWIW I use this: 1/2 headwind up to a 10 knots increase of bg and if you have a tailwind of greater than 10 knots use min sink.
In all honesty though, when in doubt fly best glide. You have enough to worry about when your engine shuts off. Thinking about all of this crap for an extra 1/4 mile will likely leave you flying by perfectly good landing sites for something only marginally better. This stuff is great to discuss and debate, but unless you practice it constantly (glider pilots) you're likely better flying best glide and expending brain power elsewhere.