More I think about it, the more I suspect they're gonna push to sign a FA QB. Reasons:
1. Rams don't have a lot of draft picks to play with. If they trade for a QB it's gonna be worse and they still need to address OL and get a young QB with upside.
2. Dropoff from the trade option QBs to the poor FA QB class isn't too great. Sanchez, for example, knows the offense and while he won't wow anyone is there really an appreciable difference between him and Glennon? That dropoff needs to be considered along with losing picks. Hoyer, Mallet, Locker, Moore, Gabbert etc aren't inspiring either, I know, but still the goal is depth and competition among those names for Bradford not finding Drew Brees.
3. Rams have been bit by FA OL additions. Meanwhile rising teams like Dallas have demonstrated that getting your OL pieces in the draft can provide immediate dividends.
4. OL group in this draft is one of the deepest positions. Even if the Rams need to address OT, OG, and C they can pull it off given the availability of interior OL well into most drafts and certainly this one.
5. Bradford contract re-do will enable them signing one OL FA along with a vet QB since none of these guys are gonna command big bucks.
6. If teams get stupid on the QBs the Rams do consider in FA they move along to OL and proceed as we have already expected them to.