Why not buy a replacement GPU for your 2011 machine off eBay or Amazon?
Don't get me wrong if you wanted to upgrade I know you will enjoy your machine but a GPU costs much less then a entirely new machine.
Replacing the logic board and/or GPU would be cheaper (assuming my amateur diagnosis is correct), but given that it's 5 years old, I'm OK with moving on. Any excuse to get something new...
There are repair shops that'll do a flat-rate logic board repair for $150-180. I'll probably sell the mini "as is - for parts" on eBay and let someone else take advantage of one of those services.
I remember when the life-cycle of a Mac was much shorter...I went from a PowerMac G3 to G4 to G5 in a span of 6 years. Either that or my needs (and abilities) have already peaked!
I haven't ordered my new iMac yet (waiting for the right config at the refurb store), but after playing with one at the Apple Store, I'm actually very excited. This will be my first iMac.
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