I'd use the reverb and one of the delays set to the most prominent 'kick' that you hear on the records with the same timing as whatever Hank had his set, at the correct level and balanced with the reverb so in the mix it would give the impression of a multitap machine if that's what it was. I've messed about with it as if that's my only option and I have had very pleasing results. If you get the tone and gain right, along with as close as possible to Hank's playing style, it does work and I'd go as far as to say I could do a pretty good job with it if I had to. A lot of the Shads hits have the echo so low that it is the reverb that makes the sound what it is, along with compression. A prime example of this is the verse part of Atlantis, though the multitap is evident on the plinky bits. If you listen to Shindig and Dance On, it's more reverb and compression that repeated echo. I always said that The Sound of The Shadows is very apparent on Move It and they are not even there at that time, nor is the Meazzi Echo or Vox Amp. It's the studio reverb that provides the magic on the lead guitar that we all love. It took me a lot of re-listening to the original tracks to realise a lot of this, but Hank's use of echo was not as pronounced as some would have you believe.I think many of us have been guilty of 'over cooking' the echo volume - me included. It's all good fun and you never stop learning.
The following day, I rang early and was no. 11 but still got nowhere as all the "emergency appointments" had gone! 
(Knock on your door, ring on your bell, tap on your window too!) Luckily, my symptoms are fading, so back to usual soon hopefully!