I'd be plenty happy with one- or two-switch forward or flyback. Push-pull is undesirable due to the lower current draw and doubling of voltage. I think transformers are also less available (unless that doesn't matter because it's a one-off, I don't know). Half bridge would be okay as well, but kind goes too far the other way (dividing the voltage in half and doubling current). And full bridge is just too much complexity for so little power output, I wouldn't bother.
So, what's been mentioned above, or an old fashioned UC3842, or a handful of other things that don't immediately come to mind that I'd have to shop for, would be likely suspects. For the two-switch inverter, use a dual bootstrap gate driver.
Definitely a buck regulator isn't suitable here; the SW node is never rated much more than 2V below ground, and only for short transients at that. Likewise a boost regulator won't do, but a flyback/SEPIC/Cuk capable type will. External switch, boost or buck, non-synchronous types may also be suitable.
FWIW, active-clamp forward seems to be the most popular among fractional-brick DC-DC modules (which you might look into if you don't need to make this circuit for special purposes). Though they also seem to have terrifyingly bad efficiency at light loads, at least the couple I've seen. Noisy too -- that's another thing the two-switch configuration helps with, reduces EMI.
Tim