Welcome to the fold!
Yes, and yes to your queries: YES, it appears that baking the video card seems to be the solution with the greatest effect and longevity and YES, Apple will charge for ANYTHNING related to your machine due to its age (mine is a mid-2010 27" iMac i5 with the same issues)!
I may reluctantly have to set aside time this weekend, to accomplish this tedious repair, myself.
Elsewhere on these forums, mention is made of a class-action suit filed on behalf of 2011 MacBook Pro owners for these very same issues: Perhaps we should inundate those legal representatives with our identical difficulties, and they could emend/expand their suit to include us, too?
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The plaintiffs are represented by Gary E. Mason, Steven N. Berk, and Esfand Y. Nafisi of Whitfield Bryson & Mason LLP, and Michael Ram of Ram, Olson, Cereghino & Kopczynski. For more information about the lawsuit, contact Esfand Nafisi by email at enafisi@wbmllp.com or by phone at (202) 640-1167.
The name of the case is Book et al. v. Apple, Inc. No. 5:14-cv-0476 (N.D. Cal., filed Oct. 24, 2014)."
http://9to5mac.com/2014/10/28/apple-class-action-lawsuit-2011-macbook-pro-gpu-gr aphics-issues/
http://9to5mac.com/2014/10/17/2011-macbook-pro-gpu-complaints-not-going-away-as- petition-reaches-18k-signatures/
http://www.cnbc.com/id/102129683
http://www.macrumors.com/2014/10/28/macbook-pro-2011-graphics-lawsuit/
http://appleinsider.com/articles/14/10/28/apple-hit-with-class-action-lawsuit-ov er-2011-macbook-pro-graphics-failures