Which of the stations in Jordan as accessible?
Is it possible / feasible to take a bus from Damascus and then once over the border in Jordan head to the first station and catch the train the rest of the way?

I realise it'll take longer but it sounds a lot more scenic.

Alternatively (or in addition) how about travelling from Amman and heading south, towards Petra (I realise the track doesn't stop in Petra, but somewhere in the south), maybe Aqaba?

There is further information here: http://www.seat61.com/Jordan.htm