John,
The fine threads have nothing to do with resisting oil leakage – only fine to increase sealing pressure as the cap is tightened. The seal is between the gun lip and the ‘gasket ‘- if the gasket (seal ) is a complete circle (not a washer), If the gasket is is a washer, the oil may also leak between cap and washer.
I would be using a resilient gasket material such that it is not overly stretched as the gasket is forced against the cap. A washer type gasket would avoid any stretching and may work more efficiently, even though there are two surfaces to seal.
Starting point is flatness of the lip on the barrel of the gun (assuming the threads are actually parallel on both barrel and cap). Next, be sure there are still threads available when fully tightened (Is the seal actually thick enough). Seal material may need improving.