I vote no for an adjustable stem. Use one of the Satori Heads-Up risers,1-4, there are usually a bunch selling on eBay. If the bars are too far away just get a cheap replacement in the 70-90mm length, Titec or a used Thomson. I might change the bars, but ergo grips are very nice, comfy. Do the saddle last, see what riding position you settle on before you demo saddles. Get good tires, I'd pick something out of the Continential trekking or urban line.
Leave the fork alone. Even a worn shock does fine on pavement, if you go rigid you might not like the road chatter. If you want to carry loads and have eyelets on the rear drops put a Delta Sherpa on the back; fairly light, strong and cheap.
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There is more to life than simply increasing its speed. - Gandhi