I just found another review where the customer is running the EVGA 750 card on a 300w power supply... maybe you want to roll the dice and try it out?
Here is his review:
This card runs is very quiet, much quieter than my CPU fan at 50% (I don't hear it). At 55 watts maximum, I didn't need to upgrade my 300 watt PS. I got this instead of the 750 ti because I don't need the extra CUDA cores (not using Photoshop, or Roxio, Nero, etc.) and only needed 1GB of memory instead of 2GB since I don't game much (the extra memory would only seem to help when playing games at higher resolutions). Maybe I could have purchase the overclocked version, but I mostly watch videos (YouTube, Comedy Central, etc.) and this improved the image quality a lot, especially in full screen mode compared to my onboard HD4200 graphics, though these drivers seem to need some extra time to improve the image quality sometimes, like when starting to watch videos at full screen (1400x900) on Comedy Central for example.