In general, I can't imagine what month reform could be done that would be worth the pain of switching. Computers are doing all the hard calculations now. While calendars throw programmers for a loop sometimes, what really nails programmers (and therefore computers) are timezones and all the screwy things we do with seconds. Changing calendars is orthogonal to those problems, and the possibility of real reform on that front is more likely, since the costs/benefits work out more pleasingly.
Saying that it doesn't matter because computers do it for us is just hiding dirt under the carpet. I agree that timezone and second adjustments are more problematic, but having a more rational overall approach would also help there: you would have a "hack zone" where to dump all the madness (the special 1-day/2-days period), making it easier to deal with any adjustment. Currently, you are inserting most changes on 1 January and / or 31 December, but then also hacking February for no particular reason, all the while not being able to use the week as a meaningful unit.
Throughout history, we experienced periods when people would not shy away from bold cultural and rational changes in order to improve life for future generations. Holding the (adjusted) Gregorian calendar as an ultimate taboo is just sad.
The first chapter of Daniel Boorstin's The Discovers has an interesting history of calendars and time-keeping. For the question of Why a seven-day week, start on page 13:
http://books.google.com/books?id=aEr07wJ21NYC&lpg=PA13&vq=7%...
tl;dr The week varied among cultures, and the seven-day week was in use by the Romans by the third century. Each day of the week honored one of the seven "planets" (in the ancient use of the word, a wanderer in the sky): Sun Moon Mars Venus Mars Mercury Jupiter Venus and Saturn. Derivations of those words are still in use today.
It seems like that would complicate the business practice of dividing your fiscal year into quarters. I guess each quarter would be 3 months + 1 week but then you don't have quarters starting/ending evenly with months.
Today if you pay a monthly fee for something, the daily cost varies month-to-month. Why should things cost the most in February? While it may be true that fiscal quarters won't be aligned with month boundaries, they are more evenly spaced.
12 months has the benefit of dividing the seasons into 3 month quarters. However having an uneven number of days per month and with the solstices and equinoxes falling somewhat haphazardly on the calendar, this doesn't seem like a good reason to stick with the current system.
As long as we're redesigning the calendar system, I think the solstice and the equinox should fall in the middle of a season with the Winter Solstice effectively marking the start of the calendar year as a holiday. The leap day could be the day that proceeds that, effectively being used as a day to mark the end of the year. Seasons would then define periods of similar daylight.
The only reasons not to adopt this sort of calendar are ceremonial. Having a 13 month calendar simplifies so much from financial calculations to having consistent day of week/month boundaries that I can't see any real down sides.
I have no idea how to promote widespread adoption of a new calendar, but it is something I've thought about a lot.