To my mind the things in play are lateral-location (precise alignment of the coil in the magnet gap) and damping/over-damping (bolt tension).
One thing to understand here is Tannoys of this era are complex hand made/assembled devices. The predate ultra-precise modern production techniques so do have a degree of imperfection. As an example you will almost certainly find a different number or combination of card spacing washers under the compression drivers left to right, even different types (e.g. brown are a different thickness to white). These were chosen at the factory to position the compression diaphragm at exactly the right hight from the pepperpot, so whatever you do don’t mix them up!
Another thing to consider/experiment with is how tightly you have the drive units bolted to the baffle. If you are using a traditional thin-wall Tannoy-style cabinet, i.e. with the drive units mounted from the back to a rather thin baffle over tightening them sounds absolutely horrible and does really mess up the treble/make them over-bright/forward. I have mine with plastic washers under the bolts on the back and just very gently nipped-up so they can’t move, little beyond finger-tight. My guess is this allows the thick rubber front gasket to add some damping to the baffle rather than the metal basket directly coupling and energising it, but whatever the reason it sounds hugely, hugely worse tightened up too hard. This has proven true both with my previous DIY York cabs and my current Lockwoods. Certainly play with this.