Whew you got a lot of input there to digest!
The only thing I'd say, and this is of course a personal opinion- if I were doing it, on the terms+ objectives you explained, I would focus first, maybe most, on new wheels (maybe new hubs if you want+ can get money), and MOST DEFINITELY go to a fully modern 9-speed Hyperglide geartrain. And I'd try koolstop brake blocks before doing anything expensive or complicated to the brakes. And if you DO decide to replace the brake levers, do seriously consider brifters- integrated brake&shift levers. They are astonishingly easy + convenient while riding- and more-so, the more shifting and braking you do. I'm American but lived 70 miles SW of London (between Farnborough + Portsmouth) for 4-5 yrs and rode a couple 1000 miles on our tandem with my wife. Whew did we USE that geartrain a LOT, all day, every day. Oh! did we appreciate a fab wide smooth reliable setup.
Here's why focus on wheels and HG -
The frame's a given, it's been in the family 40 years. It is, what it is, nothing you can do to change/improve that. But you invest in the continuity of your family's bike that's important to you (and I think it's cool too, I've done the same with an old Schwinn Twinn from my mom.) But, that makes the wheels the next best, and arguably the ONLY, way to improve the performance, handling, and responsiveness of the frame. And new+good wheels (and new+good tires) will certainly have a noticeable impact- worth the cost.
Geartrain performance is the next largest impact on rideability, enjoyment, and "mission" flexibility, and even more-so with more shifting. Unless your aunt+uncle are out in Norfolk/Suffolk/Essex, they're probably gonna do a WHOLE LOT of gear changing, unless they ride on very different territory than the short-and-sharp up+down, twisty, narrow roads that we mostly rode on there. And they'll do even more shifting+braking with age. I say "do it right for them." It'll feel TERRIFIC to build 'em a great bike on which they enjoy many happy miles and long years together as they grow older Lord willing, and that you will enjoy in turn as well, hopefully for many years after that. I say the more THEY enjoy it, and the longer they enjoy, the more YOU will enjoy it when it's yours. For me it gets more special to me, the more special it was to them.
(one guy's opinion, you get to choose).
Back to the bike- If you've ridden with HG, you'll appreciate the positive impact on shifting, rideability, flexibility of terrain, power, etc. (If you haven't, I'd urge you to try one that's set up RIGHT before you decide against it. I'm o-so-pretty-sure you won't regret it.) From the sound of it, you're replacing wheels, brake levers, R der, + cogs already anyway. The net increase in cost to go to 9-sp HG isn't big. ("performance-to-cost" you said.) Spreading the rear drops of an old carbon-steel frame is readily done. I've heard that 9-speed is less finicky and more forgiving in setup+shifting than 10 (altho I myself have only built+ridden 9sp). It's certainly cheaper- over here you can get used Shimano 9-sp kit on ebay and new, high-quality non-OEM parts for far less than new Shimano. Chains last longer and are cheaper.
One last thought- they (aunt+uncle) (and maybe you) might also appreciate inline gear position indicators, at least on the rear shift cable, maybe on both. We love 'em, and the more shifting back+forth on the back and the front, the more we love 'em. You know where you are, helps avoid the crossovers, can get on the right chainring ahead of what's coming up, etc. You can do it without taking your eyes off the road to look down+back, potentially destabilizing the bike or getting disoriented. I cut that little 1 inch cable down to 1/2 inch so the ferrule butts up against the body of the indicator to eliminate compression, and file the ends to get a little angle between the ferrule+ indicator to help cable routing.
http://www.amazon.com/Shimano-ST-700.../dp/B001GSSE5I
($15 here, Amazon won't let me go to amazon.uk)
That said, I've heard not everybody likes them, so your build, your decision.