How about the chest for Arena doesn't attribute to Silver but it has its own counter
How does this work? You play the mode normally. You turn in a chest then your team has 1 chest turned-in. Now, the other teams need to score a chest turn-in point (or the winning team can turn-in a chest for an extra point - thus helping secure a win).
At the end of the round, the winner goes to the team that has the most chest turn-ins.
If two or more teams have an equal amount of turn-ins then the team with the most silver in that category win the match.
Its clear that Rare take awhile with this game mode, so this idea would probably be for Arena 3.0 next year. We can't even get a much needed increase from the 1000 Silver in our current game mode.
But in the future, I think having the chest (or if they add more in the game mode) would work better if it wasn't attributed to the Silver mechanics. I think the silver point system is fine for those ships as is and it will play in part to what I already described. And this change would mean the chest is much more valuable in its own way.