I am unaware of XLR adaptors that will allow you to utilize the extra gain of the balanced ouput. Perhaps they exist. … but most will just halve the balanced output, effectively being RCA to RCA in that regard.
There are 1:1 transformers made by Jensen and others that will allow you to use XLR to RCA and retain the gain, and also a nice device that I have two of: the Decware ZBIT.
The only way to properly take a single ended termination to a differential requires more than a balun, and seeing that the issue is more than just inserting a potentiometer. It has to do with dealing with the symmetric signals. Bus gain structure will also suffer.