I've lived on the Monroe for 42 years. I'll be hunting it for mule deer this year as well. I don't bow hunt anymore but I can help you find deer here.
Monroe is not known for a lot of mature deer, (some call it a mule deer nursery) because almost the entire unit is covered in two track roads and relatively flat on top. Yet, like any unit, there are always a handful that are killed every year. We had a big burn two years ago, on the north east end of the unit, and a few very good bucks were killed in that areas last fall.
We had a fair amount of winter loss in the spring of 2016, but there doesn't appear to be a problem with winter loss this year. That means, I think, there won't be a lot of two year old bucks to hunt, but their will be a fair number of yearlings.
I don't think you will have any problem killing "a deer", killing a mature deer will be a considerable challenge, but that's the sport of it. If you could take home a wall hanger without much effort, it wouldn't be much fun, after a few years. ;-)
I know about 2 thirds of the unit, pretty much backwards and forwards. If you're interested, I'll give a "head start" when you come, if I'm here. If I'm not, I'll circle some locations you can check into, on your U.S. Forest Service map. If you know when you're coming to scout the unit, I'll be able to tell you if I can show you around a little.
We are a high desert, so our water holes are full some years and bone dry other years. This is starting out as a wet year, but it can be powder dry but August. I pretty much know where the water is and where isn't, I will give you some info on the natural water and the livestock tanks in various areas.
It will likely be hotter than the hubs of hell in August, however, you are probably going to be hunting between 8,000 and 10,000 feet, so the nights are always cool (not cold). Unless it's raining, which is rare in August, it will be in the high 80's and 90's most every day.
If you have any other questions, let me know, I'll do what I can to give you a little help.
DC