Pardon me if I'm about to prove myself a clueless American...
Do you have a store (local or chain) that gives you (small sums of) cash/store credit for old games? I got $15 back for my original Forza disc, and used it to pay for half of the new Forza Ultimate discs, which includes all of the DLC and a few extra cars in addition. Even without that, $30 is easily cheaper than buying all of the DLC available.
Also ,just in case anyone was wondering, you can't use the original Forza 3 disc with a Forza 3 Ultimate car pack installed.