If I was being laid off, I would look for an external job, especially because you say that none of the internal roles seem to be good fit to your skillset, and the internal roles you qualify for are roles that may be on next round's chopping block.
My thinking is this...if I'm a stellar employee that the company loves, they would have found another role for me. I.e., like the first time they got rid of your job and transferred you to a role on a different team.
If they're giving me a pink slip, it means that:
1) They don't love me enough to keep me. I don't bring them enough value to be worth keeping.
2) The company may be on shaky ground financially and who knows whether the next internal job I get will be cut in a year or two.
Plus, if I apply for external positions, I may be able to negotiate a higher salary.