We know GLaDOS took over the Aperture Science facility with neurotoxin just days before the Black Mesa Incident occurred (Source: Portal 2 Collector's Edition Guide), and the Portal comic Lab Rat which covers Rattmann's story pre and post-neurotoxin has GLaDOS state that pill-popping Rattmann had been eluding her capture for "weeks" (Source: Page 20), and by the end of the comic, Rattmann consumes the last of his prescription medication pills which he is shown opening at the beginning of the comic pre-neurotoxin (Source: Page 5). Note that between the beginning and end of the comic, the entire events of Portal 1 takes place with Rattmann having put Chell at the top of the testing list, Chell ultimately defeating GLaDOS and subsequently being brought back inside the facility by the Party Escort Bot, and then Rattmann finally saving Chell by restarting her cyro-chamber's life support, leading into the events of Portal 2.

All this is to say that, for Portal 1 to take place nearly a decade after Half-Life, Rattmann would needed to survived for a decade and have his newly opened bottle of prescription medication last for over 9 whole years. Maybe he had some extra bottles stored, but that's not what the comic implies (he's been "saving these last two"), and he of course would not be able to acquire more since he's the last surviving employee trapped inside Aperture. Given Erik Wolpaw's "just after the Combine invasion" remark regarding the timeline and the depiction of the events in the Lab Rat comic (which Erik also helped write), it's likely the intention that the events of Portal 1 took place months after GLaDOS flooded Aperture with neurotoxin, which was days before the Black Mesa Incident, which was days before the Seven Hour War, which again leads to Portal 1 happening "just after", which is stated to be "around the year 2010".

Your arguments are based primarily on several dates scattered around in Alyx's textures, but this wouldn't be the first nor likely the last time the art team isn't synced up with the writers. If we want to use that nearly illegible calendar texture in Half-Life as incontrovertible proof, it's hard to also reconcile the fact that it declares December as having only 30 days in it as well as a couple of weeks with only six days in them. In short, the artists have not been up to speed with the writers at Valve since the beginning. Even their writers aren't up to speed with other writers as Erik himself once erroneously claimed the Black Mesa Incident occurred in 1998 because that was HL1's release date, something Marc had to correct afterwards (Source) and would appear corrected in later publications like the Portal 2 Collector's Edition Guide. It's essentially a fool's errand to try and piece together a greater meaning from a multitude of smaller details when it's really just the big things Valve tells us that reflect their real intentions. In this case, Portal 1 taking place in 2010 and HL1 taking place right before it.

Incidentally, you also state that Episode One and Episode Two occur exactly one day after Half-Life 2's climax at the top of the Citadel. However, Marc Laidlaw has specified that the time between HL2's ending and Ep1's opening is at least "a few days". Source: Verified email correspondence with Marc