After much frustration this is what I did
Step 1: When All Else Fails, This Will Fix It.
I went rummage sale shopping for a replacement to my 21 year old lawnmower. The engine on my old mower was in perfect shape , unfortunately the carriage was rusted and is really not safe to use anymore. I was hoping to find a junker with a good carriage and swap motors. As it was I came across a relatively new mower for a very low price ($5). When I asked if it worked, the owner sheepishly said that she used it for 2 years, then it started surging and would die frequently. She spent $60 at a repair shop and it lasted another year and now it's back again. She just wanted to cut her losses (hence the $5 price). I gladly took it off her hands 3 years ago. Unfortunately for me my engine mounting holes did not match the mount on the chassis. So I went online, found suggestions to replace the carburetor gasket and membrane..... no good. Replace the throttle springs....no good. It would surge at idle between low and high speed and anytime I would hit a thicker patch of grass it would nearly die. I wasted about $15 for the parts. So here is how I fixed it and have used it for the past 3 years without a hitch.
First a little safety. This will void any warranties. Of course, pull the spark plug boot anytime you work on an engine. Use common sense. If you have gas leakage, do not attempt.
Second a little theory. This particular engine is designed to run at an optimal speed. The engine fan creates air pressure against an air gate which is mechanically linked to the throttle. At the engine starts to work harder, the fan slows, there is less air pressure on the gate, which in turn allow the throttle springs to open the throttle for more gas to increase the engine speed. The throttle springs pull on the throttle constantly trying to increase the engine speed. The throttle spings work against the air gate. When the potential energy of the throttle springs equals the air pressure force on the air gate, that is the speed of the engine. It is now at optimum r.p.m. The engineering objective is for a constant speed no matter what. You can mow thick grass in one area to idle shortly after and the engine maintains the optimal speed. Hence there is no throttle cable on these engines. Great in theory, maybe not so much in daily operation.
My fix has been this. Remove the air gate linkage, remove the throttle springs. With a variable speed drill, widen the hole in the throttle for the carburetor. A word of caution here. The throttle is plastic. Go slowly, do not force the drill, be careful that you do not break or crack it. You might start with a bit the same size as the hole and increase the bit size 1/64" at a time until the hole is right screw size. The original hole is small, good luck finding a matching screw, hence enlarging the hole is likely required. THE SCREW NEEDS TO HAVE A POINT ON THE END. Screw in the pointed screw into the widened hole. I used a small wood screw. You will have to play a little with the setting to find the optimal speed for your engine. A good place to start is a point about halfways between full open and full closed throttle. At this point turn the screw to where it makes contact with the plastic carburetor housing. You do not want to insert it into the housing, it is just to keep the throttle from moving. Start the engine and test. If it runs too fast, turn off, back off the screw and close the throttle a little then turn the screw down again to hold the throttle position. After a few minor throttle tweaks you will find the optimal running point, then you are done.
Sorry that I only have pictures of where the throttle is currently set. I threw away the springs and the air gate linkage before starting this instructable. Hopefully it helps someone with their troublesome engine. I took the air gate off. You would probably not need to do this. I know there are people saying it should be fixed right at a professional repair shop. However, this is a fix that has worked fine for me for a long time now. A co-worker also had the same issue on his lawnmower. Has worked fine for him also.