Thanks for the additional details
Swapping the PSU will be no problem but the room that you have for the card will limit your options I`m afraid, the HD 6950 dimensions for example are 10.24" x 5.6" x 1.65" and the better cards are larger again.
It is good that you already have 8GB of Ram and in all honesty for your intended use any more than 8GB will be a waste of cash as you will not be running any form of software that will utilize it.
I will see what I can find graphic card wise based on the dimensions that you have provided.
FWIW: If you were not tight for space you could get both a good video card and quality PSU for your $300 budget.
Couple of cards that will fit http://www.newegg.co...N82E16814161395
As an alternative you could upgrade your case, video card and PSU for under your $300 budget http://pcpartpicker.com/ca/p/oRjM
Edited by phillpower2, 23 November 2012 - 06:19 AM.