Dhl,
To take your first paragraph, ALL cartridges (except for a very few, among which are some early Deccas and probably some others of vintage origin) are inherently balanced. The typical modern cartridge does not know or care which side of its coil is referenced to ground. Since historically 99% of phono stages were SE, most cartridge makers label one of the two pins per channel as "ground", just so that the two channels will be in phase, I guess. When we use an SE phono stage, we then treat the signal as SE.
But I did think some about your other point, whether connecting the shield to the negative phase would convert the signal to SE. This only comes up if one is using a cable that was built for handling the signal as SE, but now we are connecting that cable to a balanced phono stage. If the plug is RCA, then the negative half of the signal would have to be carried on the ground side, as far as the phono stage is concerned. As long as the "ground" side of that RCA is connected to the negative phase of the balanced circuit (and NOT to chassis ground, as is the case for your PS Audio), I don't think it would make any difference that the shield was also connected to the negative phase (it would not actually be grounded and so would operate as an unshielded cable). The shield is typically only connected at one end. But this is really a hypothetical situation; if one has a balanced phono section, one should use a balanced cable (two wires for signal, one pos one neg, plus one wire for ground) terminated with an XLR plug.
I know nothing about your PS Audio GCPH, but I take your word for it that you are listening in SE mode. Sounds like it is not a true balanced circuit, if the RCA jack is connected to chassis ground. Or if the circuit is balanced, they don't want you to operate it as such.