It might be that you'd be better off with a battery
(capable of >1A discharge). Supercapacitors are
not especially cheap, but simple. Many modern
batteries are not overcharge-tolerant and so
would need charge control and a capable
switch (could be just diodes, if you're lucky).
If you architected your supply around the need
for hold-up, could be easier - line to battery is
one section, pretty common charger design with
enough upside current to handle the
through-load-current when line is up, and then
battery to output as a regular ol' buck?