Hi,
The biggest problem I have with this is I can't replicate it or it is not close enough to my two previous experiences to allow them to work.
However I will recite both of them.
One is mentioned in one of the Threads you linked to when I found out my wife's iPhone had iMessages turned Off somehow (it was accepting SMS texts)
The other was on my own iPhone. The Number, whilst still being greyed out to say I could not alter the setting, was turned Off and only my Apple ID was active.
This meant the Mac sending from my Apple ID could not iMessages the iPhone Number (it would sync the Send the Mac did on the Apple ID And I could reply to my Apple ID from my Apple ID so it looked like it was working).
The first was easy to "cure".
The second is a bit more involved needing a reset of the settings for Messages on the iPhone.
Remove the Apple ID form the settings.
I then set the phone to Airplane mode to break with the servers for a few minutes.
On returning to the settings I made sure the iPhone Number re-registered when I turned Messages On.
Once that was certain (I tested with iMessaging the Apple ID which would be the Mac).
Then I re-added the Apple ID.
The AppleGothic Font is something that was found recently.
It is needed in the iMessages registration Process on the Mac.
As far as I can tell this is redone each time the Mac or the App is restarted (based on the info in the madrid.plist)
Via the other threads you seemed to have covered the other possibles:-
Date and Time Issues (including Router and Time Zone)
DNS issues (I must admit to not using Proxies for iMessages - iChat never did well with them to the AIM Servers).
Keychain First AID.
PRAM/NVRAM resets
In the Contacts App > Preferences > General Section there is a Region setting.
I believe this sets the Country Code for the telephone numbers stored in Contacts (if they don't have one in the first place) although my testing as writing this appears to not support this. (I am sure somewhere effects this).
What happens in another Mac User account or the Guest Account ?
I did convince someone to create a desk top folder and do that long winded move half the .plists out of ~/Library/Preferences and then restart apps to test then place 1/2 the moved ones back then repeat until you find the group that might contain the suspect .plists
They had success with this but did not say which .plists they felt were involved.
The iChat app would not launch properly if the Address Book My card was incorrect.
There are similar issues in Messages.
Messages does need the full country code on iPhone numbers in order to send iMessages properly.
Most people close to you don't give a country code as part of the number.
Something within the whole set up does this for you but right now I can't seem remember or find out which setting it is.
It is late where I am and it will be a while before I am back.
(I will stick to the Thread).

10:14 pm Sunday; August 10, 2014
iMac 2.5Ghz i5 2011 (Mavericks 10.9)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad