ReadyNAS appears to boot by itself

That is definitely the right supply. The switch and power socket you can see on the outside of your NAS are not the ones on the supply itself. You will also need a 6" extender for the ATA power connection (unless you want to cut off and splice in the original cable). I also cut short the other cables and installed the 90° connectors from my original supply (since it was totally gone). If you want to keep the old supply intact as an emergency spare, you can find the 90° Molex connectors on eBay. You could just use the ones pre-installed on the replacement, but that will leave you with a lot of extra wiring in the chassis.