As mentioned, power transformers are slightly overwound, to correct for sag due to losses in the windings and core.
120:28VAC looks like 4.3:1 turns ratio but could be closer to 3.7:1 (assuming 15% regulation) so running the transformer backwards can give lower than expected results.
That would give, with 28VAC in only 104VAC out. It depends on the transformer's quality.
edit: large 1kVA transformer, assuming better 5% regulation would give, with 28VAC in only 114VAC out. (assuming 5% regulation)
For your power levels, running transformers at mains frequency means they are bulky and huge.
Modern inverters use high frequency SMPS to step-up to HV DC and then commutate that to a pseudo-sine wave.