The Sony ‘XM4 unfortunately doesn’t support aptX/aptX-HD codecs (unlike the older ‘XM3), so you’re rather stuck with SBC unless you invest a fair bit of cash.

LDAC transmitters are now available, but they’re not cheap. Check out the FiiO BTA30 Pro on Amazon. To be honest I’m not sure what else there is at the moment. LDAC receivers are much more commonplace.

FWIW discrete AAC transmitters don’t appear to exist at all. 

Of course if you don’t need to go wireless you could always wire the ‘XM4 directly to the Port’s analog outs, assuming the headphones are in active/powered mode. 

Thanks for your reply.
If I choose the FiiO BTA30 Pro, would I need any other leads? And what leads would I need to plug the phones directly into the Port?

I don’t know what leads the unit comes with, nor what you might have in stock. You’d most probably simply want a digital coax cable from the Port.

Again, it’s fairly obvious. The Port has 2*RCA outputs. The ‘XM4 comes with a lightweight short-ish 3.5mm male/male cable. I have no idea how far from the Port you’d want to sit, but presumably you’d need a fair length of something converting a 3.5mm female to 2*RCA male. Possibly a 3.5mm extension cable combined with a short 3.5mm female to 2*RCA adapter cable.