Let me have a noob's go on this one:
Why don't you use batteries for the +5V and -5V?
As I understand, you are going for a temporary solution, right?
If so, you could use your PSU for the +12 V, and two 9V batteries in a center ground config, effectively giving you +/- 9V.
Those rails could be used for +/- 5 V DC with the 7805 and the 7905...
Voltages are floating, so you could connect center ground with the PSUs negative for proper reference.
Another option:
Use an old ATX power supply, which supplies you with +/- 12 V DC and +/- 5 V DC.
Shouldn't that work to read that EPROM?