How to step up unregulated ~0.2-1V to regulated 5V
Basically, you're in a bad position.

Using your specified approach, a simple 3-phase rectifier just won't work: at the lower end your AC voltage is not nearly enough to overcome diode drops in your rectifier. Even using Schottky diodes a minimum peak voltage less than about 0.5 volts will not produce a useful current out of the rectifier.

ThePhoton has what seems like the obvious alternative, which is to boost the generator output using a transformer and then rectifying and regulating the output. There are two problems here. The first is the relatively large voltage range (5:1) of the generator output, although this can be dealt with. Much more of a problem is your generator speed. 150 to 800 rpm will give generator output frequencies in the range of 2.5 to 13.3 Hz, and finding transformers which will operate at these frequencies will be a good trick. At the least, they'll be big.

I'd recommend increasing your gearing ratio by a factor of 20 to give a range of 3000 to 16000 rpm. This will give an output frequency in the range of 50 to 267 Hz, which fits nicely in reasonably standard transformers, which you can get with 50 Hz to 400 Hz capability. In doing so, you'll up the output voltage to 4 to 20 volts, and you should be able to make a fairly standard DC supply from that. Depending on your exact current requirements, it may well be necessary to use a slightly higher gear ratio to get adequate voltage at the low end, but you're at the low end of the available frequency range anyways, so that should not be a big problem electrically. Mechanically may be another story, but hey - it's just gears, right?

You won't be able to get standard 3-phase transformers in the low power range you want, but you won't need them. Just hook your bridge to the generator directly.