I agree with the OP's plan. It's better to get all of the traveling out of the way. Initially I was going to do a night or two in Tokyo and then head south, but I saw that splitting my time in Tokyo was a real waste of time.

One problem with activating the pass on the first day is that the OP *MUST* be on the 6.50pm Narita express, to catch the last Hikari going to Osaka. Two hours should be reasonable, but any delay will mean he's stuffed. Just buying a ticket means you can use Nozomi and depart much later.
That said the posters above are correct. The 4th is a far more costly traveling day than the seventh. Your choice really.

Why are you changing hotels in Tokyo too? Seems like a real hassle to me.