but the IIsi Power Supply Unit seems very hard to get.

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Are they really that hard to get? Have you checked these suppliers?

http://www.retrotechnology.com/herbs_stuff/m_parts.html

http://www.recycledgoods.com/products/Apple-699-0567-IISI-Power-Supply-Sony-APS-06.html

Which were the orginal specs (allegedly underpowered) of the IIsi PSU, just in case I could hack a non-Apple one?

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The one that I have and that looks like it came from IIsi has following specs:

Apple Part Number: 699-0567

+5V = 6.8A

+12V = 0.8A

-12V = 0.3A

+5V = 1mA (PSTRICL)