Are you sure the input impedance is 11 ohms unbalance and 100 ohms balanced? They are way too low to be practical. Input impedances are usually measured in kilo ohms. Please recheck.
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In rereading my question, I realize I forgot to ask one more thing; or perhpas it needs to be asked in a different way. Even if the XLR to RCA adapter idea could be done, that isn't really balancing anything is it? And, therefore, doesn't that mean that increased input impedance for the amp could not be realized?