Jensen makes a box that’s incredibly handy to have for these scenarios. It takes SE / RCA inputs and converts to balanced / XLR outputs via transformers (you will also need an extra IC). I have this and can confirm its transformers are transparent enough to improve SQ versus just feeding "half your amp" via RCA => XLR adapters. Great to have in your audiophile toolkit!
Ralph Karsten of Atma-Sphere @atmasphere (I’ll try not to get this wrong but I’m no authority here) will probably point out any amp like yours is not really "balanced". A true balanced amp should take any input, even an SE signal on its XLR inputs, and still operate fully differentially. To achieve this, the amp needs a differential input stage. This can be done either with transformers (like the Jensen box), or with special active circuitry. Amps that use an inverting opamp on their RCA inputs are to be avoided - that’s not a proper differential stage!
When high-end headphone’ing was a "new" hobby, the first balanced headphone amps did not have differential inputs. Later on the Kevin Gilmore designs starting using "Super Symmetry" (SuSy or SS for short) input stages that are just wonderful - RCA, XLR, or even SE on XLR: it’s all fully balanced throughout. NO performance penalty for RCA inputs or SE-on-XLR (besides whatever noise & aberrations the signal may be subjected to on the way there via cable). I believe the DIY community even released an SE-to-Balanced conversion box using this circuitry (all discrete, very linear). Most of the electrostatic headphone amps (Stax) also have differential inputs.