I would use XLR cables and the current equipment is all RCA.I guess you already know that a balanced cable won’t get you any performance improvement?
If it’s something you need to do temporarily, I’d try inexpensive adapters, like those sold by Lynx. You won’t notice the difference from the costly ones.
Remember, you’ll need different adapters at each end to match the differing genders of XLR used at the ends of a balanced cable.