Hi,
Some friend! I hope he is giving you some sort of compensation for your efforts!
The radiator is secured to the engine, not the body, so loose engine mounts is unlikely to cause the top rad bracket to break, unless the engine is really flopping around and the radiator has hit the body!
I reckon the rad is probably loose on the bottom mounting bracket somewhere. Tighten/fix as required and replace the top bracket.
Cheap Tyres: Kumho or Hankook 145R10 were around $70 each last time I checked. But I would visit your local "pick-a-part" or Suzuki/Daihatsu wrecker. Early 80's Daihatsu and Suzuki shopping carts ran 145R10 tyres. You should be able to pick up a four roadworthy 145R10 tyres for $100 or less. Then have them swapped onto the Contessas by your favourite tyre retailer. (Bob Jane, Beaurepairs etc)
If you are in Melbourne I have four 145R10 Kumho that have done about 500km since new that I'd be willing to sell.
