I’ve called a lot to Disney trying for the military room discount. One cast member explained it in a way that stuck with me: the discounts are like marbles in a jar and the marbles get taken until they are all gone. (But, in my experience a lot of people change plans and put a marble back into the jar and then you can get it.)
I agree- room availability for the discount can be frustratingly limited. I’ve often seen the standard rooms at the Epcot/Monorail Resorts quickly “unavailable” for the discount but higher tier rooms still available. I think Beach Club also has a lot less rooms than say, Yacht and Boardwalk. And Port Orleans FQ always seem to run out of inventory ridiculously fast for the discount offers! 
Gotta say the availability for this discount seems to be substantial. Keep looking and be open!
Are we going to get a trip report at some point?
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That’s still the plan. It’s been a mess since we got back. A few days after we returned my DD2 got hit with a stomach bug. It was pretty mild and I thought it was just her belly clearing out all the crap we ate while on vacation. Then it hit me and my DS7…hard. Meanwhile, DS5 got a pretty gnarly respiratory infection/cold. And for 2 weeks we just passed it all around among the four of us. My husband worked about 80 hours each those weeks just trying to avoid being here!!! It was the sickest we’ve ever been in this house. Poor DS5, his birthday was a couple of days after we got back and his party was supposed to be the following weekend. We ended up having to reschedule his party twice and didn’t have it until after Christmas. He was so sweet and understanding about it though. So anyway, yeah, once I get caught up from the trip and all the sick and the holidays, there will hopefully be a trip report!!
I’ve always found (in 3 big trips) that whatever we end up getting with the discount works out well for us. The first 2 times it was definitely not my first choice hotels but they turned out great, b/c all Disney on site is great. The 3rd time I was being more selective b/c I really wanted AOA and ended up booking 2 other hotels first until that one came open. But we would not have paid the price without the discount.