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I believe what you are looking for is a feature in 2009. As for other ways to dimension it, there are a few - datums, detail view, move dimension to actual feature, etc.
When working with standard linear dimensioning, the only accepted method for rearrangement is a "slanted" dimension per ASME Y14.5M. SolidWorks does provide for this dimension type. To set it, select the dimension in question, then hover your cursor over the end of an extension line and note that the cursor feed back will change to a "slanted dimension". At this point, simply select the end point and drag to either side dropping in a position that clearifies your dimensioning scheme.
I tried what you described and I can drag the extension line but I don't get a cursor change. Interesting because the help file for that says it should change too. Thanks for the help. I dusted off our office copy of the standard and found "oblique extension lines", I probably knew that at some point but sure didn't remember it until you mentioned it.