Something different, getting a great power factor (> 0.94) is a good first step: you can’t simply top off your caps (which shaves off the top of the AC waveform.)
If you can arrange that you draw down the caps quite a bit and then charge them slowly as the AC rises and also as it falls you can get a better power factor. You can further lessen the draw at the peak by adding a “soft” voltage doubler in parallel to provide power at the peaks and when the voltage crosses zero (well there’s a full fullwave rectifier there, but you get the idea.)
There’s no free lunch: as the power factor gets better the regulation suffers at the top level supply: taking longer to empty the caps means the voltage falls more but you are drawing current to refill them over that longer time. You couldn’t do it this way in a power amp.