Isn't Littlefinger's sigil a mockingbird? The Titan of Bravos was his father's.
That's still House Baelish's sigil. Plenty of people create their own sigils for themselves. Garlan and Loras' sigil is different from their own house's.
Littlefinger changing his sigil is all about being looked at as helpless. Little fingers are seen as the most helpless part of the body. He wants from the start no one to think of him as a threat, merely a friend to all.
And aren't there other families with the Titan as their sigil?
And aren't there plenty of giant sigils and giants without sigils?
Can't think of any. I think Umber may have a giant as a house sigil, but that's it.
You post like everything you say is certain to happen when we all know that GRRM laughs at anyone who thinks they've got it all figured out.
This is the only theory I'm mostly behind that I feel confident in.