You need to have two PS2 Memory Cards for this to work. Sell all the cars you've won/acquired except the one you want to modify in the Slot 1 game but save the game afterwards to Slot 2. Use the cash from the sale to ramp up your car and save the game to Slot 2 again.

Now load the game in Slot 1 (the game that still has all your cars) and ask to trade with Slot 2. Once you finalise the trade, you can save the game to Slot 1 and copy the Slot 1 GT3 game block to Slot 2 and repeat the process.