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Yes, they're canti's. Agreed re. the permanent uphill...
The downtube shifters are friction. I will get this confirmed by a LBS, but I assume that this means that the rear mech will be able to shift the extra few millimetres for the greater number of cogs? Once more, I assume that they don't just push the cogs closer together (?!)
I may take you up on the aria drum brake. I will seek to use the existing drum though because it's not worn and the drum to frame spacing (for the attachment) is likely to be irregular.
Changing wheel size will have implications on your brakes though (are they canti's?) Also you don't want a smaller wheel on the back than the front because no.
I suspect you can quite easily upgrade to more gears. I see downtube shifters, are they friction or indexed? If the former then it should work straight away with a new cassette and rear derailleur. Otherwise it might be worth updating the shifters to indexed 8 speed or higher.
If you do go for a new rear hub and need a new drum, I have an arai drum brake sitting in the cupboard that would like a new home.