I think that a problem with the coolidors, is that there is no spanish cedar lining in them. The main reason Spanish Cedar is used in humidors is that it helps control the RH. Spanish Cedar likes 70% humidity and will draw from or put back in to it's surroundings to keep it there. It provides more of a stabilization effect than anything.

Your coolidor already provides a good seal - so, making sure the spanish cedar has a tight seal is uneccessary.

However, you may want to find a piece to lay on the bottom or even come up the sides with it.

It can only help the situation.