No, on the gravel....long term not a good idea, any bedding would sift down into ti..
Ditto the 'general drainage issues'.....
....might want to cover your run with a solid roof.
Where are you that you get 90" of rain a year?
Here's a great description of contents and how to manage organic 'bedding' in a run or coop...and there's a great video of what it looks like.
Ohhhhhh thought you were quoting from this thread<smackhead>You have to click on the quote box to see your whole quote with the link. I just checked it
(I shouldn't have been so lazy and made that easier to see)