Tyrion's attempts at courtly intrigue may have failed, but what if he had chosen to pursue romance instead of playing the Game of Thrones alongside the other Lannisters? Spoilers ahead.
"She comes out with a massively twisted (and spiteful) version of the truth..."
Is it really twisted and spiteful though? Shae thought she was more than just Tyrion's whore, but ultimately Tyrion was never going to let Shae be more than that. Tyrion chose his family in this game and like you said, he trusted the wrong people. He should have trusted Shae.
Alexander Robles agrees, saying, "Seriously. He should have left with her. The fact that he didn't was his worst mistake." But other readers aren't so sure. LambicPentamter notes that without the Lannister power behind him, Tyrion would be at great risk:
The only way "trusting Shae" was going to benefit him is if he left for Essos.
And as we've seen multiple times, Tyrion only has as much power as he does because he is noble born. His status as a dwarf would have ruined him many times over by now if he didn't have the last name Lannister.
In Essos, the name Lannister means nothing. He will be a dwarf, and without his vast stores of money to boot. For starters, there is a very real risk that he will be enslaved as a mummer. But there is also the question of Shae and just how enamored with Tyrion she would truly be if he no longer had any power—let alone if he was reduced to a person who is viewed as less than a man.
Lynx counters that she thinks Shae's proposal that they run away together suggests that she is truly in love with Tyrion:
I think TV Shae is truly in love with Tyrion the person and not just his money. If she was enamored with his money, she would have settled with being his whore and live life comfortably.
LambicPentamter has doubts:
Perhaps. I'm not sure I buy the idea of a person who is truly in love with someone else doing anything that will obviously result in their beheading, no matter how spurned they were, but I agree that the show has really portrayed Shae as fond of Tyrion beyond his money.
Of course, therein lies the rub—as it's her job to appear to be fond of men because they pay her.
But Craig Michael Ranapia notes that Shae likely had good reason to testify against Tyrion, even if she was in love with him:
Oh, I could very easily believe that. Shae is a low-born whore. Not exactly the most valued and respected pieces in the game of thrones at the best of time, and she knows that all too well. So does Tywin and Cersei. Love is all very nice, but it's not all you need - a head firmly attached to your shoulders doesn't hurt.
So is there a scenario in which Tyrion and Shae could have lived happily ever after? Given Tyrion's sad romantic history, could he have given himself over to love? Would he really leave the rest of the Lannisters if he felt that he could survive without them?