To me the charm of the old 3 speeds is the riding position and handling that you get with the slack angles you won't find on a newer frame.
I recommend finding a garage sale 3 speed and replacing the steel fenders with plastic ones. Steel bars, stem, cranks and rims are all heavy and can be replaced with alloy components.
Dimension makes a "Cruiser" bar that if you cut about 2.5" off the ends, and use a stem with about an inch more extension than the stock one, will exactly duplicate the ergonomics of the original North Road bars. Your local bike shop can order the bars and alloy rims from QBP. They carry Sun CR18 rims rolled to the 3 speed size (ETRTO 590) in 32, 36 and 40 holes. If you get a 3 speed made in the Nottingham plant, BB threads will be 26 tpi instead of the standard 24tpi. A framebuilder, or a very well equipped shop, can run a 24tpi tap through to allow a modern BB spindle to be installed. You may need a spindle for a 73mm BB shell instead of the more common 68mm. The Kenda 26 x 1-3/8" tires roll quite nicely without high pressures.
There is a gent here in Minnesota who intends to put a bike into production using alloy componentsts, Planet Bike fenders, a 3 speed Sturmey Archer and a chrome moly frame. It will have 26 x 1-3/8" tires and classic 3 speed geometry. I rode the prototype, and if feels just like a really light Raleigh 3 speed.
http://bikesmithdesign.com/temp/05Thistle.jpg