Heinz R you are very welcome.
You are correct that the overall crossover has to be balanced in terms of component selection to ensure it sounds "right" for the driver in question. This of course means that the Tanoplas vs twin Hard Edge surround will result in a different sound.
Interesting that you mention the choice of Tanoplas vs Hard Edge surround as when I had to replace the surround on the Canterbury's I gave it a lot of thought and in the end kept it original especially as it is the original cones from 1988 that are fitted to mine. That said, if you decide to replace your surrounds with the twin Hard Edge it is possible and there's the other option to use the new "blue" cones that Lockwood supply and which were fitted to the Prestige Canterbury HE / SE.
Interestingly, I have a pair of HPD385 which are almost identical to the 3889 used in the Canterbury with the exception that the physical flare profile of the HF horn is smoother (better machined) and I believe the magnet material composition is slightly different i.e., HPD is Alcomax V whereas 3889 is Alcomax III. The HPD's are fitted with an upgrade that Tannoy used to offer (via Lockwood) called THEOS whereby blue cones with the Hard-Edge twin roll surround from the Canterbury HE/SE were fitted to the HPD 385; Lockwood still offer an upgraded blue cone but not sure how it differs to the THEOS version (they used to offer for the HPD 315 12" many moons ago but now discontinued).
I have the matching upgraded crossovers to accomodate the Hard-Edge conversion and as you'd expect the 6.8 µF (C1) that you queried for the Canterbury is 5.4µF on hard edge surround version of the HPD and 5.6 µF for the Canterbury with Hard Edge. I used an active crossover though built by a UK valve aficionado called Nic Gorham of Longdog Audio. Really well built and based on the circuit here:
https://www.hilberink.nl/codehans/tannoy86.htm.
Regarding the Canterbury "as is", the existing caps in the crossover are all RIFA MKT metallised polyester so should not need changing...the 2.2 uF is a Philips chicklet Polyester film capacitor. Modern caps may provide more clarity but that might be at the expense of the vintage sound.
The Canterbury 15 is from a golden age, the pair I have were the first ever built and a one off called the "Prestige Royal" (before they chose the name Canterbury) and suffice to say I will never part with them.
I might however be fitting my upgraded HPD's to one of the sets of modern Tannoy Legacy Arden cabinets I got from the Tannoy factory in Coatbridge before it closed - a little side project if you will. Anyway, good luck with the Canterbury and I'm sure you'll have them back to spec pretty soon. You may even be able to get new old stock on e-bay if that is an option.