How to make paper waterproof
There are various waterproofing sprays and brush-on treatments sold for maps.  They shouldn't change the colour very much, (hopefully not at all for print) but may darken the base colour a little.  Here's one example, and here's another.
The key to using these is to ensure perfect coverage, and several thin, even, coats.  The same would be true for spray lacquer, which should also work though it's not necessarily designed to be flexible.  For origami I'd spray from a different direction for every coat, but even so getting it into the crevices will be tricky.
I've also seen a recommendation for polyurethane varnish, with the note that some change the colour but others don't.
A dip process would ensure good coverage but in an oil-based varnish is very likely to change the colour (as you found with epoxy), maybe adding translucency.
A range of options is presented here including some I've mentioned above.  One that looks particularly interesting is shellac.  It dissolves in alcohol but not water, and hardens when the alcohol evaporates, so unless you have alcohol-soluble colours on your paper, it shouldn't have much if any effect on the colour, and is described as being suitable for a bath process.