Welding is a terrific idea [Guitar manufacturers take note]
but in practical terms a little beyond the scope of most home DIY enthusiasts.

One alternative I am prototyping at the moment is to entirely remove and discard all strings.
Then with use of a long metal ruler and fine tip indelible ink pen,
carefully draw 6 [or 12 if you are an advanced player] parallel lines along the length of the fingerboard from nut down to bridge.

The stumbling problem I am encountering at the moment is that bloody big hole in the centre of the guitar body....

This needs some more thought... stay tuned...