If frequent application of lube has become necessary, perhaps its time to rewind the gasket. With extended use of charcloth, tiny carbon particles work their way into the fibers and interfere with sealing. If you care to send it over for a check up I would be happy to give an overhaul.
Unfortunately, the gasketless design also needs lubrication.
If freedom from lubrication is desired, I suggest O ring seals are the way to go. While these are clearly not traditional, they do seem to perform very well and require far less attention and maintenance as compared to cotton string. We offer the TinderLite models with O rings and we can make the wooden models with them as well. The TinderLite pistons have screw-off piston caps and can be had with an optional fire steel inside the shaft. Sorry...end of commercial...