Thanks for the replies. Our family mower has been down for the last six weeks, and two acres of Ohio grass is pressuring me to get this fixed. I only know what I know, and that's pitifully little. So, thanks for your advice and patience. It only has 550 hours, so I really think it's worth fixing.
I've been working on quite a few issues with this engine. I've got the Briggs Repair Manual, Operator's Manual and Parts Manual. They're very specific about the 380700 series, and that's where I got the instructions for setting the carb. Briggs is insistent that the adjustments are done on Low at 1200. We do always run the mower on High at 3600 (when it used to run, anyway), but Briggs says to do this work at 1200. Are they wrong? I went back over the manuals and couldn't find anything about always running it at 3600. I'll give them another search tomorrow for that instruction. I don't want to do this wrong.
I'm confused about the factory settings. This TK carb has (1) idle speed screw and (2) idle mix screws. In addition to setting them while at 1200 idle, Briggs says that factory settings for this unit are CW until hits slight resistance and then CCW 1-1/2 turns for idle speed screw and CCW 3/4 turn for both idle mix screws. The manuals say to hold the throttle plate against the idle screw while making the adjustments. (Hard to do when they put the air duct over the top of everything, but we're trying.)
That's when someone told me that the throttle plate should always be touching the bottom of the idle screw when the dash lever is on Low. I even tried lowering the idle screw until it touched the plate (thinking I had it too open), but it doesn't touch the plate even when completely closed, so that's a no-go.
So, I'm more confused now. Does the throttle plate in that photo look like it's in the right place, then, nowhere near the bottom of the screw? Unfortunately, since they don't touch, turning the idle screw does nothing at all. The engine just keeps surging and eventually shuts itself off. And it just sits in the 1300s, at that, because I can't get it down to the 1200 it needs. I'm sure it wants gas. Replaced the fuel filter, removed carb and cleaned thoroughly, replaced air-cleaner-to-carb gasket, new air filter + plugs + oil filter, checked hoses, replaced valve-cover gaskets (lash was spot on as it stood), replaced dipstick tube and seals, etc. All B&S parts, as called for in the Parts Manual for this particular model, from reputable parts stores.
Before I can go any further, guess I'm stuck until I find out where that throttle plate is supposed to sit. I'm game to set the carb screws, but so far turning any of the three of them has no effect on the engine at all. (FWIW -- starts like a dream.)