There are three major certain blocks of story passage here:

Arrival in Tokyo & six weeks
[01]-[06] E3 - E3 starts on Thursday, it works out nicely if this is that day P&L went.
[07]-[09] airplane - Leave Thursday night, be in Tokyo in the morning. Saturday morning because of crossing the date line.
[10]-[12] - spent Saturday shopping etc., can't go home, [12] shows it is dark out.
[14]-[36] - find Tsubasa in the morning, spend day at Tokyo Game Show (which runs Fri-Sun), go back to Tsubasa's place.
[37] panel 1-3 - Monday morning. Tsubasa leaves for work.
[37] panel 4 & [38] - Six weeks later. 42 days, plus or minus, but let's just say exactly 42. Monday again.

Bookbag day & Railcard day
[42]-[74] - [42] starts with new shirts on our boys, definate two day period. [73]-[74] might be the following day but is probably at the end of railcard day.

Chapter One minus 1 = Sunday
[80] panel 4 to [129]

Now, the space between six weeks and bookbag day:
[41] - only appearance of those shirts, so is its own day. Minimizing time sets this as Tuesday, bookbag day as Wed, and railcard day as Thur.

post-railcard, pre One-1:
[75] - morning of some day, is probably railcard+1=Friday but could conceivably be the following Mon or Tues.
[77]-[79] - Any time after Yuki sends that e-mail, but soon after really, as Piro wouldn't wait very long to check his e-mail.
[80] panel 1-3 - Any time, but Junpei's computer is still there so probably not too long after railcard day.
All things being equal, [75] to [80] should be Friday, Saturday, and Sunday morning in the space between railcard and One-1, but...

Those pesky throw away references to passage of time:
"After several months, he remains stranded in Japan" - if [10]-[12] is day #1 and we follow the suggestions above, One-1 Sunday is #51. (Sunday [14]-[36] is #2 plus seven weeks or 49 days = 51) That's still a bit shy of two months, which is the minimum anybody could reasonably exaggerate to "several".
"You bring [the railcard] up at least once a week." - even taking sarcastic exaggeration into account, this points at at a week bare minimum passing from railcard day to Chap One, and probably at least two.
"I found your bookbag a few weeks ago" - generally a "couple" is two and a "few" is three or more, but two still works okay.

So if you add...
One extra week puts chapter one at day #59 in Japan and makes the three girls' statements severely exaggerated but not insanely so, two extra weeks set chapter one to #66 and brings the exaggeration down from severely to very. And so on.
Given that any added time would clearly be meant as a token acknowledgement of lines of text we would rather rewrite or ignore, one week is a fairly good compromise.
Where is it best to add the extra week if you choose to do so? Probably after panel 3 of [80]. While it's certainly a nice flow to have Piro lament the loss of his sketchbook and the next day lament not having the money for a new one, having it anywhere else does even worse things to the logical flow.

Otherwise:
Chapter one is day #52 in Japan if you ignore the inconvenient statements in [129], [135], and [155].

Month breakdown?
I'm going to assume the mid point of the main bulk of the story should be essentially the exact middle of September, i.e. the 15th plus or minus, and that Chapter 7 is that mid point, plus or minus.