Oh, right!
I forgot, in most voltage doublers you use equal-sized capacitors, then the first capacitor shouldnt get reverse-biased at all.
But if you use a smaller first cap, it's going to undergo full plus and minus excursions until the second cap gets at least half charged up.
So you need a non-polarized first capacitor, which is a bit of a problem:
(1) if you use something like a non-polarized electrolytic, these tend to be made mostly for motor-starting apps, where they're only used for a fraction of a second. They'll overheat and boil-over if used for more than a few seconds (trust me).
(2) The other non-polarized electrolytics tend to be for cheap speaker crossovers, where they're only rated for a few volts. Don't think of using these either.
(3) If you use a non-electrolytic, a 50uF 300 volt one will be kinda big and expensive unless you shop at surplus stores. Avoid the ones that don't say "NO PCB's"!!!
Or I've heard you can put two electrolytics of twice the size in series-opposing and that acts somewhat like a non-polar capacitor. This sounds mighty fishy!
So to summarize, my idea is SUPERB in theory, but a bit difficult to implement unless you have an uncle that works for the power company and gets to carry away "used" capacitors.