To my knowledge, no Damned has ever taken the Heaven's Blessing option. And I don't know any well enough that have graduated to even know if it was presented as an option to them.

And I wouldn't frame taking the Liar option as escaping.

Every Heaven graduation is considered another miracle for the Liars. It gives credibility and belief to their cause. And Thia is trying to make herself into the next god. So it suits her purposes well enough.