You might want to try making another vent liner, this one with the cone on the inside leaving the outside flat the way the White Lightning liner is made.
Although an exterior funnel shape looks like it will direct more of the flash from the pan into the hole in the middle so it is a good idea, that's not necessarily true.
We are talking about the gas from pan flash moving at a very high rate of speed. As such, it is possible for the gas to deflect off of the coned wall towards the center of the liner and converge right at the vent holes mouth. In this location, it can create a high pressure zone that blocks off the gas that was trying to enter the hole in a straight linear fashion from the source of the gas.
In other words, the cone may keep the pan flash from getting thru the vent hole.
There are reasons that things like vent holes on the old original flintlocks don't have exterior cones.
If there weren't reasons, we would see vent holes with cones on the outside of the barrel on thousands of the old original guns. Instead, what we see is the exterior of the barrel left in the same shape as the rest of the barrel in that area. In some of the old guns the builder did go to the trouble of forming a cone on the inside of the barrel that led into the vent hole.
The easiest way to do that without installing a dedicated vent liner, was to drill completely thru the barrel wall opposite the vent hole and then to drill about half way thru the barrel wall where the vent hole was located. After this internal "cone" was done, the hole thru the barrel wall opposite the vent hole was threaded and plugged with a screw.
On other old guns, the builder used a special little machine made with several small gears in a line with each gear driving the next one and the "outer gear" connected to a crank. The gear furthest from the crank was fitted with a small rotary burr cutter which formed the cone from inside the bore.
That's a pretty fancy little machine but with the improved speed of the flintlock gun that had this machining done, the builder appearently thought it was worth the effort.