I once had to service one of The Shadows' units - they used Watkins Copicat tape loop echo devices. I think Watkins now do a digital version, but I don't know if they have modelled all the drop-outs and other noise to give it the classic sound.

Ah, the WEM CopiCat and those darned tape loops. Technology marches on, eh? As a (bad) guitar player, I can tell you that there's nothing like getting your "sound" down from the beginning. The "vibe factor" you get from the echo or spring reverb in your rig makes a big difference in how you play, at least it does for me. I use an old Roland Space Echo for that now, plugged into an old Fender Bandmaster. Personally, I don't think that I could play "dry" and then re-amp the track or add plug-ins. But as a recordist/mixer, I also like to have options available to me after the fact.
So, I say go for your actual sound in realtime, just do a lot of pre-production to make sure you're getting what you want onto the "tape" before you commit.

Doesnt this very scenario represent the reason to have a Direct/Thru box available as well as a couple of amps or tone generators of some sort???!!

In the digital world where tracks are cheap and easy to come by in large numbers, it only makes sense to play the part with ALL the effects you could ever imagine the song to need , as well as taking a dry signal out to another source and also recording this simultaneously.

This way, you get the 'vibe' of the effected track coming back at you through the monitoring as well as sending a mixer friendly track to the recording system.

I listen to the effected sound while I'm tracking as it DOES add to the vibe of the track. The dry track simply gets printed, it has the same nuances of the players mind, and it can be used in the future in a very cohesive way, be it standing alone, backing double of the effected track or simply a track that can be reamped back to the effects or even another different sounding amp if need be.

Just my take on this.

Thanks for the ideas! The doubled signal could actually solve my misery. That would give me the necessary options in the mixing stage. I could route the dry signal back to amp and tweak the sound as much as needed. Or, if there was only a dry/wet balance issue, I could just add a bit of dry signal to the good one. Given that it doesn't produce phase problems.

Have you looked at the Fender '63 reverb tank? It's not authentic to the Shadows, but its a pretty reliable unit that I've seen a couple of surf bands use. As with all the modern Fender tube units, you can tweak them - rebias the tubes hotter - put in NOS tubes - if you are so disposed. But it sounded like a pretty good piece stock when I've messed around with it in stores, and I'd be inclined to get one if I was working on retro stuff.