I've had several Crisscross models (one step below this one). Nice bikes!
I would go either trekking bars or drops. Trekking bars would be the lowest cost option, as you could continue to use the twist grip shifters.
Trekking bars came standard on those bikes in 1993.
http://www.trfindley.com/flschwinn_1..._Cnsmr_17.html
Headsets are cheap (less than $!5). I would just replace it myself.
+1 on narrower tires.
Nashbar trekking bars and Nashbar Moustache bars
http://www.nashbar.com/bikes/Product...2_175533_-1___
http://www.nashbar.com/bikes/Product...75_-1___202348