Put another check in the "reset" the bevel column.
Just go back down to one (or two if you want) layers of tape and hit the DMT 1200. You may have to retape the spine occasionally as the tape wear down, but it really is the best solution, no regrind necessary.
Oh, and if its a true wedge, you'll have to put the tape in the exact place every time you tape it, since the edge of the tape is what contacts the honing surface on a true wedge (maybe you've already noticed that). But if there is any concavity to the blade you should be fine.