Did that check valve have a schrader valve on it and did you replace that? Do you have a air volume control on the side of the tank? Do a search online and look carefully at the mechanical needs of a bladderless tank. You are looking for a drain down valve [probably in the well] a surface check valve with a tire type valve on or near it, and a air release valve on the side of the tank. I would start by changing the 25$ air volume control valve [air release valve] on the tank side, or removing and cleaning it out. Prone to failure in many ways.
After that, think about the pump check valve.