17.5 HP Briggs & Stratton Carburetor Adjustment

I am trying to get a riding mower back in operating condition.  It is a Briggs I/C 17.5 HP engine single cyl model 31C707 engine.  I replaced the carb with one I got from Jack's (part #594593) and the engine starts up.  It idles fine, but when the engine revs up past about 1/2 throttle it begins to run rough, stumble and the exhaust starts to show black smoke.  I assume it is too rich a mixture, and needs an adjustment.  There is a screw with a hole in it on the top of the carb body (not the idle speed screw) but that is the only thing I can see that might be an adjustment.  Is this an adjustment screw?  I tried to rebuild the carb, but wasn't successful, so I got a replacement carb that is slightly different in appearance. I have also replaced the Magneto Armature, since the plug wire was bad. 
 
Any suggestions on what to do next?
Thanks

The model is 31C707
Type is 0603B2
Code is 090803ZA
 
The part number of the carburetor said it was obsolete, and no longer available.  This one was the replacement recommended, and the engine Model & Type was listed as covered by the replacement part number. 
 
It was originally a NIKKI carb, but when I tried to rebuild it I wasn't competent enough, and it didn't work.  When I tried to re-assemble it, it wouldn't let fuel through to the engine, and I think I messed up the way the jet fit with the solenoid that shuts off gas when the ignition is turned off.  Then I messed up a gasket that was not included in the rebuild kit, and that allowed gas to leak into the manifold.  I gave up on the rebuild, and bought the new carb.  The engine runs, but not at high speed

Thanks for the tip about checking the choke.  I hadn't thought about that, and I will check it.  I probably shouldn't have put the intake manifold on before I started it, and it would have been obvious if the choke closed.  I am kind of new to small engine repair.  I will be out of town this weekend, but will check it next week when I get back. 
 
Thanks for the help.

Thanks to everyone for the help.  I checked the choke today, and it was not opening properly.  It was catching when I put the air intake on the carburetor, and would stick with the choke closed.  I worked with it a while, then added an extra gasket between the carburetor and air intake and adjusted the position of the air intake until it released and opened properly.  I started the engine and it runs like it should.  I ran a 1/2 tank of gas through it mowing, and then made a minor idle speed adjustment and it works like it should.
 
Thanks again to everyone.
 
Mike