It's a good find from gophert. The remaining issue with specifying a new transformer is that the current rating could be different for each output.
A transformer will usually last almost indefinitely. 12 years isn't significant. If something has caused the transformer to short some of the windings it will get hot, but there could also be an external short. If possible, I would suggest disconnecting the low voltage connections and leaving the transformer connected to the mains for an hour or so to see if it gets hot. If it's no more than warm after an hour, and the output voltages are about right, it's working fine. With no load, I would expect all the output voltages to be around 10% higher than the numbers printed on the transformer.