Sorry to say this but you're measuring the axle [slightly] the wrong way. You need to measure the overlock nut dimension, i.e. outer distance between nuts. We can deduce this by taking 145 - 5 - 6mm = 134mm but maybe not quite as accurate as it's three measurements taken. That dimension really needs to be 135mm. Looks like you are 1mm out. Yes, a washer behind the nut should solve it.
On another note, the last position cog is a mile from the spokes... but I don't think/see there's a way to easily change that on your freehub (without grinding something).