I had some minor issues with the same problem when my Hawk was first used. Here's what I did on my 2013 Hawk with outside shower. I hope my experience helps you:
Crank the hot water all the way open at the faucet handle (outside) and crack the cold only slightly to get your desired warm temperature. You will only need a little bit of cold to get 'warm' water for a shower or to wash your hands etc...
This should give you the proper results, however one caveat is that you will be wasting water if you don't use the knob on the top of the shower handle for you to take 'Navy' style showers. (For all the non-military types out there, the navy shower is a short burst of water to get you wet, followed by shutting the water off and soaping up. Then, blast the water onto your body (hopefully warm!) to get all the soap off. Then, shut the water off at the shower-head for the next person.)
I take lots of hot showers this way with no cold/hot fluctuating water issues like you mention above. Not a day goes by when I'm camping that I don't get a nice hot shower. As a note, I do carry a small pump to draw water out of any nearby water source (boat ramps at lakes creekside, etc.) and a Grolsh beer bottle with small chlorine pellets to drop into my water tank and treat the water before use. We don't drink it but just use the tank water to wash dishes and shower with. We can top off our tank in about 10 minutes time including setup of the pump & strainer to draw water. On a 3 night camping trip if my wife and I both want hot showers, we draw & fill the tank only one time by outside source. On a week long adventure we usually draw twice, unless no water source is around. In that case - wet wipes are your friend because you have to skimp on water!
Play around with the wand and faucet handles to assure you're getting the pump running all the time with no fluctuations. Don't trickle the water out but use the shutoff knob on the shower head to control when you need the warm water.
I hope this helps.
Kilroy