I agree, finding a set of already built single speed wheels would probably be a lot less of a headache, and quite possibly cheaper than re lacing those rims. Look on craigslist / ebay frequently... they pop up a lot and you can really get a good deal.
I know that sometimes people run into chain line issues. They seem easily resolved with spacers behind the cog, and or bottom bracket length.

A lot of guys will take off the second chainring. I think this sometimes requires a spacer? Never done it, so not sure. But that's something to look into if you're not looking at replacing the crankset.

Don't get me wrong, I like conversions. And I don't know the value of that bike... but it looks pretty well kept over the years. Does everything function well? I usually only consider already cannibalized bikes for a conversion. Maybe consider keeping your eyes peeled for just a frame set? Or a used ss/fg frame you could build up? It's your bike though! I'm not trying to discourage you from proceeding, just tossing another idea into the mix