What's you're looking for is a colourless clear finish (referred to as 'water white' often in finishing circles) and there's an easy solution here, which is waterbased polyurethane.
These are very different from the polyurethane that you've already tried, their only common element being the added polyurethane resin.
Don't panic when you open the tin, they are milky-white when liquid (as with most waterbased finishes) but dry completely colourless. Do watch out however for ones tinted to match the colour of traditional oil-based varnishes!
In addition to the colour, or lack thereof, these have other advantages you'll like.
Fast drying — again as with most waterbased finishes waterbased polys dry fast enough that, depending on your drying conditions, you can put on more than two coats in under an hour, and often in 30 minutes.
Low odour — these are a low-VOC finish since most of the liquid component is water. While they do have a distinctive smell it's not strong and most people don't find it unpleasant, the majority of users are comfortable applying them indoors in their homes with no particular care for ventilation and it is generally completely safe to do so.
Water cleanup — any equipment used or spills can be cleaned up using water. But note that once dried they are very much not soluble in water any longer :-) Warm water is better than cold and it helps if it's soapy so add a squirt of dishwashing liquid or hand soap if either is handy.
There is one disadvantage worth noting:
Raised grain — because they contain lots of water waterbased finishes will raise the grain of the wood when applied, which means your lovely sanded wood will go from silky smooth to rough. If you want the boards to be ultra smooth when you're done you need to pre-raise the grain by dampening the wood and lightly sanding back after they have dried (you can speed drying using a hairdryer if you like).
Some people do this more than once to be on the safe side. The most I've heard of is 5-6 times, but I've never found any advantage to doing it more than twice in comparisons I've done.
Remember you only need to sand minimally, just one or two passes with light pressure using a fairly fine paper, e.g. 240-320 grit. If you sand more heavily you'll undo the benefit (because you've sanded too deeply into the surface) and the finish can then raise the grain.
Some additional notes on application.
I wouldn't use natural-bristle brushes to apply these. If using a brush use a synthetic, either made from fine nylon (often amber-coloured) or polyester (often white). They don't work well wiped on with on with a cloth. If you prefer not to brush use a foam roller.
Don't thin. Unlike oil-based finishes where thinning is often used and highly beneficial waterbased finishes tend to work best at the consistency supplied by the manufacturer.
