New tyres and the kitchen sink
I don't see a problem here; do you (well apart from the remaining rust stains on the washer reservoir.
I have thought long and hard about tyres. I used to have Yokohama A008's on my MGB. They were dead sexy; the outside quarter of the tyre was basically slick apart from a row of little dimples. I have no idea what they added to the performance of the car but they did wear out after around 10000 miles.
I have eventually settled for a far more pedestrian Dunlop Monza 200 tyre in 205 65 15. The tyres have a sensible and therefore quiet tread pattern, and a bit of silicone to maybe stick a bit better. I could have gone wider with the 6.5" rims but I figure these tyres are already streets ahead of the OE ones and there shouldn't be too much lateral movement on cornering. I have stuck with a 65 profile to maintain the original wheel height both to keep the speedo accurate and to maintain what ground clearance there is. And best of all, at $110 fitted balanced and the old tyres removed from the old rims, they're CHEAP! You don't get that often with a Jag!