This topic has been beaten to death, but what the heck lol. I have the same set up, GH stream sluice with the powerhead. While a bilge will work, I'd recommend gas powered if feasible. Bilges will work, but they're rough on a battery, so.be prepared for that. I have used a 2000 gph bilge on my sluice with the low flow mat, and even with a steeper angle, it had some trouble exchanging material, material being classified down to 1/4 inch before being ran. It works, but is slow and the incremental processing time takes longer, time equals drain on your battery. A 3000+ gph bilge offers a little more *mmph* for processing, but more wear on your battery. Remember, Docs mats love fast "hot" water, not deep. So the smoother, low flow matting is great for bilge work. Using the regular mat with a bilge for smaller placer gold is like using a shark hook to catch a bluegill, its overkill and slows your flow down a bit and hold up the processing speed.
It comes down to your willingness to classify before you run. With a bilge, youll have to classify, with gas you wont, except pulling out giant rocks. I have mine running 2" semi trash pump with the regular mat, just shovel and forget. Those mats will catch gold, even sub-100 fly poo in the regular matting with screaming hot water with imperfect pitch and water flow. With slower water, just make sure you give your mats time to exchange before you feed more. I go off of a 5 second rule, if my mats clear out in less than 5 seconds, im too hot, if longer, im too cool or my pitch is too low. Thats not solid science lol, but it works for me. Good luck!