Sorry, but I feel that a lot of the latest arguments are not quite thought through:
Also, you can't just get rid of Easter; no Christian is going to accept that. 
And what about Jews, Muslims, Hindi, Buddhists, ... who get useless work-free days, but have to work on their own religious fests? A much better suggestion is to remove all religious holidays, but give employees some more vacation days. This of course creates other problems of its own, but at least it respects all religions.
Come to think of it, the 7-day week basically comes out of the Bible. Kind of makes me wonder how other calendar systems with no biblical influences do weeks.
And as current dicture says that the bible are not the words of God directly, this should make you wonder how the 7-day week got to make its appearance in the bible in the first place... I believe the answer lies in the lunar cycle of 28 days. This is a very convenient time measure between single days and years, that can be checked almost every night, and where you can even measure ratios by the moon's appearance. So it makes sense to define weeks as quarters of the lunar cycle.
This really makes one appreciate the phrase "thank god it's Friday". Without the week based on Genesis with a church-mandated day of rest, we could well have ended up with a lot less free days. You can indeed thank (Judeo-Christian) god and religion for having the tradition of weekends.
I highly doubt your last sentence. If I remember correctly, in Germany we switched from the 6-day work-week to the 5-day one in the 1950s. While Germany was a lot more religious at that time than it is now, barely any change in legislature or every-day life was dictated by religious concerns. Actually I cannot even think of any religious reason for this change, especially as the bible seem to suggest working on 6 days a week. Therefore I conjecture that for any community, there is an inverse relationship between the average working hours and the technical/social development, regardless of any religious concerns.
The solution is to adopt hexadecimal, then number the days from the beginning of the year.
One week doubleweek heek is 0x10 days. The last digit of the date is the day of the heek. You can have 5 or 6 free days in a heek, which is a higher ratio than 2/7. Fix this ratio by removing Easter and other UI sins. Dates go from 0x000 to 0x16E, the first two digits of a date feel month-like. The revolting French didn't get their metric calendar past the church, but this is better anyway. :>
You completely failed to demonstrate why this change would solve any problem at all!
1) You mistakenly wrote "Saturday, April 30", but with your change you would have written "Saturday, 0x78", which is equally wrong. Sure, it is easier to see that the 8th day of the heek is not a Saturday, but what does that help? Did you intend to write "Octaday, 0x78" or perhaps "Saturday, 0x76"? And if you would just have written "0x78" without the day of the week, but meant "0x76", then noone would have realized that something is wrong here.
Note that you got the day of the week correctly, but messed up the date. So adding the day of the week (which is more or less independant of the date) adds a way to check the correctness, similar to checksums of bank accounts IDs.
2) Assume you want to compute the date of 20 days in the future, starting with May 21 or 0x8D. Do you really think that computing this is hex is less error-prone than in the current way? Sure, now you have to know how many days the month May has, but I would say this is pretty common knowledge

. In any case the errors comes from the change of the month resp. heek.
3) Finally your choice of hex is completely arbitrary: Why not use the base 7 which ties nicely to the current week scheme? Then each day of the year has a 3-digit number, and we only have to take the last three weeks of every year as vacation, because we cannot express the date any more
