However, transformers do not reflect secondary load C to the primary.
Transformers transform impedance and impedance includes capacitance. However, things are not as simple as just that. You have to also consider how a parallel capacitance interacts with the inductance of the transformer- and here we are talking about a resonance. This is also occurring on the primary side! Of course, I'm saying the same thing that Dave @intactaudio just did in different words.
If your EE friends tell you this isn't a thing, here's an EE that is telling you it is, just FWIW... but 'multiplied back to the source' is only correct in that there is a fractional factor involved, variable with frequency. This is really one reason I stay away from SUTs if I can help it 😁
As a general rule of thumb, the best advice is to use low capacitance cables. If you do this right, the electrical resonances involved will be so high that on the cartridge side it will be well outside the transformer's bandwidth. If loaded properly on the secondary side (such that there is no ringing) again you're off the hook. At any rate don't think for a minute that the loading on the secondary side (including capacitive effects) can't be measured on the primary side!