The test for compression that Briggs and Stratton recommend, is to put the speed control in the stop position, disconnect the spark plug, and rotate the engine backwards until you feel compression. (You would do this by turning the clutch on the engine's output shaft. Check which way it rotates normally by pulling the starter cord, then turn it the other way.) When you find the compression, pull on the outside of the clutch firmly in that backward-rotation direction, and let go so it rotates freely at a moderate speed and hits the compression pressure, backwards. If it bounces off the compression pressure and moves forward slightly, the compression is satisfactory. If it stops soggily when it hits compression, it is unsatisfactory.
Because you only felt a slight improvement from the oil test, your problem may not be lack of compression. B&S engines traditionally run fairly well with not much compression - they are not sensitive to it. Have you checked that the choke closes completely when you put the speed control in the choke position? If it doesn't, there is an adjustment problem.
