Is it possible to model a single-phase phase-shifting transformer in LTspice/Multisim/PSpice?
Is there a way to model the single-phase transformer to include the
phase shift (e.g. with a complex turns ratio)?

and

But suppose I want to simulate a per-phase circuit (using real values)
in a simulator such as Multisim, PSpice, LTspice, etc. and use the AC
Analysis mode

The easiest way (in AC analysis) is to set the applied voltage at the primary to have the appropriate phase shift. I don't use any of the aforementioned simulators so here's how microcap would do it: -

I expect that all Spice simulators will have a similar feature in their voltage sources. See also the numerical shorthand of a voltage source - I've set the phase to be \$\color{red}{30}\$ degrees: -
DC 1 AC 0 \$\color{red}{30}\$ Sin 0 2.5 1meg 0 0 0
Or just use a time delay sub-circuit (if working in transient analysis): -

I can't imagine that LTSpice doesn't have this.