My problem is it wants to oversteer and hence feels a bit strange for a FWD car as most understeer.
Yes, that is strange. You can at least presume something is quite wrong with the back end to get an oversteer balance as it certainly won't be caused by too much front grip
I would start by checking the tyres, are the rears shot?
Then have a look at the rear wheel alignment and suspension bushes/mounts - sensible neg camber, sensible ride height, mild toe-in, minimal suspension play etc.
Then look at the spring and arb rates - maybe try disconnecting the rear arb. Basically soften the rear off either by spring/arb or both
Maybe check the rear dampers at the same time.
It's a process of elimination, but I would leave the front well alone while it is obviously gripping.