And outside of Avila, those that do, won't be much higher than the guys they are replacing in the top 51.
This is an important point. Not every player under contract counts under the Salary Cap LIMIT.
I have been confused in the past with the exact number ... 51 vs. 53. It's top-51 contracts up until the start of the regular season but I am not sure if it flips to the top-53 contracts in September.
For purposes of this post, it does not matter.
The Rams currently have
more than 51 players under contract but only the top-51 apply to the cap-limit. If the 51st player has a 2023 cap hit of $750,000; and the Rams sign a player for a $1M cap-hit, that signing adds $250,000 to the Rams cap-limit because the $1M guy is added but the $750,000 guy comes-off the top-51.
Spotrac shows this well. If you look at the Rams' Spotrac page, you will see all the players currently under contract, along with their 2023 cap hit. At this moment (it could change at any time) Colin Duncan and his $754,000 cap hit is the 51st contract and counts against the Rams 2023 cap-limit.
The 52nd contract has a $753,000 cap hit and belongs to Timarcus Davis but it's crossed-out on Spotrac because, it does not currently count against the Rams cap-limit ... because it's not in the top-51. By-the-way, bonuses paid to all undrafted free agents do count against the cap.