The only way you will be able to power your iMac's built-in screen, with a better GPU, is to actually replace the internal GPU.
And your options will be rather limited.
The best option will be to get a 6000Series Radeon card (6970)from a high end 2011 iMac to swap out your current card, ebay would be the best bet as these cards from parts vendors are still going to be $800+ dollars in some cases for that card.