Refretting

Months ago I acquired a very old kit dulcimer that had sat in someone's closet for ~20 years.  I began assembling it back in late January and finished it up last week. The notches were pre-cut in fret board and UNFORTUNATELY I did not measure to make sure that they were in the right place ( I "ass-u-me"d that they were!).  After stringing it up it sounded TERRIBLE  The attached photo shows how far off the notches were.

I have pulled out the fret wires and have resawn a new piece of cherry to overlay on the fret board, and am getting ready to properly cut the fret notches for the VSL (using StewMac's fret position calculator). Now for my question:  Should I install the new fret wired BAFORE I glue the replacement piece onto the old fret board or wait until after it is in place?  I am concerned about pounding in 18 frets on an already finished dulci, but am also concerned about the stress that inserting the wires will cause in such a thin strip of wood (0.3" thick, or about twice the thickness of the fret notches). 

What say Ye, oh great builders of the realm?