Flattening the Sole of a #7 Hand Plane
I bought an ordinary Stanley #7 jointer hand plane at the swap meet the other day. I want to use it as a jointer for jointing (straightening and "right-angle-ing") board edges. Someday I want to buy a powered jointer, but I need something now, and it wouldn't hurt to learn hand planing skills.
The plane looked perfectly flat at the swap meet, but when I got it home and put a straightedge to it, you can see a little light shining from underneath the sole. The sole looks very slightly worn in the center and slightly higher on the front, back, and sides.
I own a set of DMT diamond stones (mostly the two-sided six-inch, but I have one 8 inch extra-extra-course DMT stone. The problem is that this is a very long plane. I don't want to make things worse by trying to flatten the sole with small stones.
Here are my questions:
1. The gap is very small. Am I better off leaving the sole alone and simply using the plane as-is?
2. If it is worth flattening the sole, then how do I do it without making things worse? Can I use the diamond stones? Do I need to find a really big piece of glass and use multiple sheets of sandpaper? Any better ideas?