Its not a ridiculous idea to take a QB mid round when you have a QB that is struggling in key areas like leadership, situational awareness and clutch play. Ted Thompson had Favre and drafted Rogers. Belichik has Brady and spent a second round pick on Garafollo. Save the argument about tail end of careers because in the big picture, it's no different than Tannehill going into his 5th year and if he fails, needing to look elsewhere.
Though I wouldn't spend a first round pick, if they engineered a trade out of that pick and used the extra pick on a QB in the second or third it's a decision I would support. If the QB they are looking at isn't available than you're all in with Tannehill and hope for the best. Regardless, Moore is an FA and they need to sign/draft a QB at some point this off season.