I'd bet quite a lot that the OP already has drybags from their DoE trips (though I suppose they maybe used plastic bags - the assumption when walking/backpacking is that your rucksack is not waterproof and you use waterproof inners of some kind to keep your kit dry).
You could try putting stuff into drybags and bungeeing it on (depends a little on just how robust they are, some of my drybags feel more robust than others!)
Yup, I use a mix of proper dry bags and sturdy plastic bags, so not too fussed about the waterproof-ness of panniers, especially considering that seeing as we have a large window of time (students) we're unlikely to set out when we know that the weather will be grim.
I learnt the hard way to waterproof my stuff when I couldn't be bothered one day (not a cloud in the sky, and was in a hurry to leave). I was half right..it didn't rain, but I fell into a river!