I would just use bleach to be honest. It's super simple and won't require anywhere near as high of a dose of prime as you think. Following these directions I would just go with a double dose. These directions are for drinking water so you could even do this for drinking.
Make Drinking Water Safe with Bleach
How to purify water with Bleach
If the collected water to be treated is cloudy and contains sediment, either scoop a new sample with less sediment, or strain it first through a makeshift filter (cloth bandana, t-shirt, coffee filter, etc..) or let it sit in the container allowing sediment to settle to the bottom. Gently pour off the clearer water on top.
Directions for using bleach for drinking water:
Use regular liquid household bleach (any brand); however the only active ingredient should be sodium hypochlorite. Do not use bleach that contain soaps, perfumes, or dyes. Be sure to read the label.
Add 8 drops (almost one-eighth U.S. teaspoon) of regular liquid bleach per one gallon of water to be treated.
Mix thoroughly and let stand for 30 minutes (important).
Then, smell the water. If the water has a faint smell of chlorine, then it is okay to use. If you cannot detect any chlorine odor, add another 8 drops of regular liquid bleach. Let stand, and smell it again. If you still cannot smell chlorine, discard it and find another water source.
Chlorine test strips are useful to verify the chlorine level in the water. The maximum safe level for drinking water according to the EPA is 4 ppm
(parts per million).