Dont try to "cheap out" on this, you'll end up causing yourself more grief and frustration than doing it right the first time. Neoprene floats and fat floats. Not a comment on you, I dont know you or your BMI, its just a statement of fact many of us must deal with. Rocks wont do crap to keep you under water, you need lead and you likely need a LOT of it!
First, have you ever spent time in this river? What are the temps like? 3 mil is fine for water about 70 or warmer, if its colder, you need thicker neoprene. If this river is flowing, you will get colder and need thicker. If its really cold and flowing, you will need a hot-water system (but thats a whooooole 'nother thread).
Second, have you ever tried to sink yourself in a pool with this wetsuit? When you find out what you need to sink, you can plan on tripling it if you have fast water.
Third, Lead is heavy and hard. Diver weight belts are made of thick nylon straps with heavy duty buckles. Try to put them in a fanny pack or tied off jean legs, will have them ripping out and you back on the surface with no way to get back down to pick them back up.
When I dredge in Colorado, the water is shallow, cold (prob 50) and running. You can walk around in it without any problem, but the instant you lay down to dredge, that flow will roll you down river like a ragdoll. After you get a hole dredged, if you stick your face up youre going to get your mask ripped off. So carry a backup mask! I also have to wear a 7mil wetsuit with 9 mil boots and 7mil hood with gloves. I could scuba dive that with about 25 pounds of lead, but I have to wear 60 pounds to dredge and I could actually use another 20 for those shallow working times. Oh, and you need special weights. find a dive shop that can melt and pour weights for you, because 7 - 10 pounders are VERY hard to find, but youd need a 20 foot long belt to stack enough 3 or 5 pounders to stay under. 2 weight belts helps carry it all.
If you can pack in a dredge, you can pack in diving weights. I recommend a game cart to wheel this stuff around.