In my experience of comparing and setting up the two sounds spoken of here, it's all possible with careful use of the controls on the guitar (whichever one) and amplifier and correct use of the echo unit. When these tunes were recorded there were no added pedals or graphic EQs, as they didn't exist to guitarists as they do today. The EQ at Abbey Road was limited but very effective and the most powerful tools I find to get close to the tone are the Hi & Low Pass Filters and Compression. Used correctly I have no problem getting the early Apache / Kon Tiki tone or the dryer 'nasal' tone of the later recordings using a Strat, Burns Marvin or even my Burns Marquee which I modified with better pickups, though the stock pickups work as they should. Also, the 'set up' of the guitar helps a lot too.
Even though I have my Meazzi Echomatic and the TVS3, I still enjoy getting my Strymon Volante to replicate that decaying echo as it wow and flutters into a musical distortion of you set it up to do that. The important part is the tone on the amp and not to try too hard by overcooking the treble. Amps vary a lot how they react to control tweaks and it's difficult to write down a set of knob positions because no two amps seem to be the same, it's a matter of using your ears, same with the knobs on the guitar, there are 'sweet spots'. I can get the early sounds on the Burns and the later sounds on a Strat - the guitars can be made to sound like ieach other.
I discovered all of this after years of insisting everything on the guitar HAD to be FLAT OUT. I unashamedly admit that I was wrong.
By listening and comparing with Hank's work I managed to get closer by listening to what the controls were doing when they were moved especially the CUT.
I recommend folks have a play around and you will eventually 'get it'.
If you have a good Vox AC-30 sound and means of adding the correct bass, treble & CUT, along with some way of replicating Hi & Lo Pass filters and a little compression ( this is where a GEQ & Compressor will help) you will find what you are looking for.