If the service center people cannot do it, you need to take your car to a local garage. You can go and check in Satwa, there are lot of ford expert workshops. They may help you.
I faced the same problem once. I went to the workshop and they changed the gear oil. He explained that sometimes the filter associated with the gear box gets damaged which in turn results into rough gear changing situation. It directly affects the smoothness of the gear change. I suppose you can start by changing gear oil and filter and see if this helps, or else look into professional gear builder who can diagnose the gearbox and recommend the repair work.
I would prefer new car than old car. One cannot rely on old cars because sometimes the maintenance cost becomes so high for an old car that it will be equal to buying a new car. So yes, New car is always my first preference.
Well there has been a log of talk about donating Mustangs for charity. DANMOSQUEDA in its recent post covered an inspiring story about how half a million for GT-500 goes into fund Brain Injury Research, we also know that nearly 2 million raised by EAA was effort to create awareness and inspire kids to follow their dreams. There may be a tinche of marketing to it, but lets see the good part.