I have a Burns Shadows Special which is quite stratty and started off on 9-42's as recommended by many. It seems that if you want to get more "Shadowy" you need to have the heavier strings (with a wound third) that Hank had on some of his guitars and experiment with effects to get the (sometimes) triple echo etc. It seems that extra effects were added in the studio, so they rarely happened on live gigs! I used to love flatwounds in the 60's as they helped with my sore fingers!
I picked up a couple of "project" strat copies last week and after a fair bit of setting up, they are settling down and are producing something close to the Burns! They had been in storage after the guy had "tried to learn", broke one, bought the other and still had no luck. It was hardly surprising as the settings were well off (double decker bus under the action gap"!). A good set up, everything stripped, cleaned, levelled, wiring resoldered, restrung and put back together within spec and they play! A bit more "cosmetic" work and they will be as good (if not better) than some of the strats I played in the 60's!