I was wrong on the type of carburetor as that one is an updraft version. I think got one still in the donor pile of equipment. It will take a day or two dig it out.Right now I got a John Deere 445 rider that I got find out what is wrong with it.
I wish I could find an IPL of this engine so I can reference it so I don't lead down the wrong path. I will try to see Briggs can provide me with a copy of the IPL but they may not even have it here in the US.
Meanwhile, the flywheel magnets should align fairly close to the coil legs. If not and you haven't physically checked the key I would suspect that it might be sheared. On the coil it should be a magneto setup so flipping it would hurt coil just throw the firing timing off quite a bit. These coils are usually labeled with one side as "This side out".
As for the compression what was the dry compression vs the wet compression of 75-77 psi. You should be around 70-90 dry. This would be high if it wasn't for the ACR (automatic compression release) bump on the camshaft. Now valve clearance being too little can cause erroneous compression readings as the ACR will cause it the engine to overly decompress.