Briggs 256707 0119 random surging at full throttle

I have a 90s model Wheel Horse 210H with Briggs 256707 0119 engine. It came with the incorrect carb. 
I have tried two different aftermarket carbs and they are sort of harder to find for this engine model. 
 
I can get the engine to idle fine. I can get the engine at WOT fine, most times. But as soon as I engage the electric PTO to start the mower deck, it surges every second or every few seconds and just overall doesn't run well. The best I can get is surging every second. 
 
Adjusting the throttle screw on the bottom of the bowl in makes it worse. Adjusting it out makes the engine want to stall. Moving throttle to choke only stalls the engine. Both aftermarket carbs I've tried exhibit similar behavior. 
 
I've even tried a low PSI fuel pump to see if it was a fuel delivery problem with the gravity fed. Nope. Same behavior. 
 
I'm not sure what to do to try to eliminate the surging.