5V 1A from 24VAC transformer with grounded secondary
To overcome the ripple from the half-wave rectifier, the smoothing
  capacitor would need to be huge.


For your current circuit you have a 47uF capacitor and if it were half wave rectified your capacitor would need to increase in value but probably only needing to double in capacitance. I'd consider doing this because it's your easiest solution.

If your output transformer produces 24VRMS then the peak voltage it will generate before and after the extra ground would be exactly the same at 34V. With a full wave rectifier your resulting peak of DC would be about 32.5V and for the half wave solution it would be about 33.2V.

With 47uF fitted the bridge ripple would only be about twice that of the half wave solution so I would say, for it to dip close down to the 8V lower operating area of the switcher, you probably haven't got enough capacitance to start of with.

It's also worth remembering that if the ripple is kept lower, the switcher input voltage will be on average, higher and more significantly the current it takes from the rectified supply (half wave or full) will be lower because IT is a power converter and when the net voltage is higher it draws less current - make use of this benefit and increase the capacitance to say 330uF, 50V.

Panasonic Series: FK Type: V 330uF, 50V is 12.5mm diameter and 13.5mm in length. Is this really huge?