What you hear and the context in which you hear it is more important than what you see. So how about the key being A minor? That one instance in the middle is highly restful and stable - if you want a 'live' ending a big Am chord is a fine place to resolve everything and 'break the cycle'. Try ending on a C - in the context of the F and G it functions as dominant and draws you back into the cycle....
I just asked this question here - what key is Dreams by Fleetwood Mac? It’s an F Major chord followed by a G Major chord….
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