I just don't see the Rams spending even a 2nd rounder for a Center

I suspect the Rams will do all they can to find a serviceable Center in FA. I just don't think they want to go high in draft capital to get one.
McVay clearly values skill players. Snead is on record as saying that if you look around the NFL, Oline starters tend to come from the 3rd round to 5th even 6th rounds.

Yes, of course, the Rams need a Center. But that isn't all they need.
I can't imagine them going for anything but a skill player at 37: WR or DB (could be Safety or C. TE on the outside if perhaps the kid from Miami should fall to 37.

I doubt they'll consider a Center until Round 4. But at the moment they are loaded with Oline players. We should not overlook the fact that they have hung on to Rhaney, who is a true Center. They wouldn't have if they thought he was not redeemable.