Crashing mid-game, every game!

Since yours does run for a awhile atleast... maybe some of this might make a difference?  Usually this is for DX crashes.

1-  Downclock the 650 a hair, maybe 50mhz and 100mhz on memory something like that

2- Set an FPS Limiter... if the game can't peg 60+ maybe try 30 just to test to see if it can run it longer.

Open Notepad.
Copy and Paste this:

GameTime.MaxVariableFps 60

Save it as "user.cfg"

You cannot have user.cfg.txt
enable "View Extentions of Known File Types" from Folder Options in Control Panel

Put it in your PvZ directory
\\Origin Games\Plants vs Zombies Garden Warfare

More things you can add to that file to play with:

RenderDevice.ForceRenderAheadLimit 1
PerfOverlay.DrawGraph 0
PerfOverlay.DrawFps 1
PostProcess.DofMethod 0
PostProcess.BlurMethod 0
PostProcess.DynamicAOEnable 0
PostProcess.DynamicAOMethod 0
Render.VSyncFlashTestEnable 0
WorldRender.TransparencyShadowmapsEnable 0
WorldRender.MotionBlurEnable 0
WorldRender.MotionForceOn 0
WorldRender.SpotLightShadowmapEnable 0
WorldRender.SpotlightShadowmapResolution 256
WorldRender.LightTileCsPathEnable 0
RenderDevice.Dx11Enable 0
RenderDevice.Dx11Dot1Enable 0
RenderDevice.Dx11Dot1RuntimeEnable 0
RenderDevice.VSyncEnable 0
RenderDevice.TripleBufferingEnable 0 

You can try changing Render ahead to 0, maybe 2 just to test.

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AMD + nVidia... shouldn't be the problem... but here and in BFH I've struggled to put a dent into them.  (even requested devs take a further look at these systems)

One guy recently PM'd me on Origin who had a system like that and said it magically started working after we tried like everything under the sun.

I didn't stick around long enough in BF4 forums to get a sense for it there.. I would assume it works fine there as the amount of people playing is sooo much higher I'd imagine.    AMD + nVidia systems I'm sure are very small minority just because when you buy an AMD cpu your likely to buy an AMD GPU... been meaning to try to check Steam's system check charts but haven't gotten around to it.

Should it be a problem?  No absolutely not

Is it though?  mmmm I don't have an answer just guesses and hunches... maybe?

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Doubt it judging by the error message but you could Uninstall VGA drivers, go to safe mode, use a wiper tool, restart install them again...

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You don't have any left over IGP from AMD left around do you?  I'd be sure Catalyst is completely gone, 100%.