Doesn't work that way. The trade chart is still king.

Trading down 5 spots only would net the Rams a late 3rd round pick.
Trading all the way down to the final pick of round 1 would only net a late 2nd round pick.
Sometimes a team will trade the pick and add a late draft pick to get equal chart value, even when trading down.
So, really, the Rams aren't going to get any more than a mid to late top 100 pick by trading down. Would they find that enticing?

The NFL still uses that trade chart pretty religiously.