The Twelfth Amendment ends with the following sentence:

"But no person constitutionally ineligible to the office of President shall be eligible to that of Vice-President of the United States."

It would seem the Constitution agrees with you.

https://en.wikipedia.org/wiki/Twelfth_Amendment_to_the_Unite...

So then, they get Ryan to be VP and install Bill as Speaker. Then they get Ryan to resign. Worth at least two seasons on Netflix.