I have since recovered from the disappointment of all of these modern sales gimmicks (and Topps has again removed card #7 from their sets), but for the missing #7's from between 1997-2005, at least, there is an affordable answer. The 2006 Topps Mantle Collection consists of 10 cards numbered from #MM1996-#MM2005, or at least from what I am aware. I currently only have two of these, but intend to obtain them all eventually to integrate into my base sets. I probably chose the worst one to start with since the border of #MM1998 does not quite match the border of the rest of the '98T set, but the rest of the '06T Mantle Collection cards seem to match their respective sets very well.
Now, comes the issue of where to place the #7 Mantle card. From about 1995, Topps began manufacturing veteran-type player cards beginning with Babe Ruth, and then M.Mantle '96, J.Robinson '97, R.Clemente '98, N.Ryan '99, H.Aaron '00, etc. Originally, I included these long retired veterans at the front of their respective team sets; then I moved them to the back of my binders with the rest of the extra cards (they're not current players!). Now, I'm considering moving them back into the front of their respective team sets as shown in the first page of my '98T set binder for the 1998 World Champion New York Yankees. There are two reasons for this: stats on the back of each card like they were still playing and recent veteran variation factory bonus cards.
This is all just part of the fun of collecting baseball cards these days.