Because architecture changes between the 2010 and 2011 the radeon HD 5750 with 1GB is going to be your best bet. Without having that level of Video support you will find your OS lagging substantially using Mac OS Sierra which already makes use of the video card processing capabilities. If you downgrade video cards expect that you may find Sierra not performing as smoothly. You may want to do a good blowout of your system.
One question do the pixels that are out of sync remain the same ones? Do they change between boots? If they are the same ones, then the pixels have frozen (often occurs from damage to the display, age or a combo of the 2) and a new video card will not alter this as the frozen pixel would be a physical characteric of the LCD screen.
If you have more substantial artifacts (sections rather than just pixels that are frozen) and happens with more than just one program. (I have found that more than one program will have artifacts until they are updated and then the artifacts go away because a software bug was the source of the issue)
Finally, and it is worth repeating that this iMac is susceptible to overheating in the area of the video card location. If you are getting artifacts suddenly, place your left hand of the back top left of your iMac display (just under the vent slit) and is this area extremely hot uncomfortable to keep your hand in place for an extended period. If so, this is a symptom that the fan is: A) Failing not properly exhausting heat from your video card, B) obstructed with debris (dust, hair, etc accumulates and should be properly blown out by someone able to disassemble and dislodge the built of debris. C) Software that is running is caught in a kernel panic resulting in overtaxing the video card resulting in the issue. D) Finally video card failure (often driven by A, B, and/or C) I actually spent $35 on a water cooling kit that I attached to the outside of my iMac aluminum case with the heat sink attachments place at the points on the imac where the heat generation occurs, Video card, CPU, HDD (this was my latest upgrade to my iMac who like yours is EMC 2390) Currently my mid 2010 houses quad core i-7 24GB RAM Dual SSD 240GB and 750 GB HDD (ODD Removed) External water cooling unit 2nd display at 1920x 1080p and primary at 2560 x 1440 and operating W10 in Virtual Machine. Like you I had a wave of random rebooting and artifacts which were tracked down to a mix of misbehaving software (kernel panic) and overheating of the video card (dirt and overtaxing of the system without robust heat management. Once those issues were resolved I haven't had issues after Sierra. (Not upgrading to High Sierra anytime soon, due to stability concerns)