Fred McKenzie wrote, on Tue, 31 Mar 2015 11:50:27 -0400:

You may find a tip that lasts longer, but it may have a problem
slipping.

I think a wine cork tip will fail within a week, but, the rubber cork
stoppers that we used in chemistry class may last longer, if I can find
them in cheap bulk quantities.

How does the tip fail? Does the metal sleeve cut through?

The metal sleeve is brand new (just put on Monday, only yesterday.)
What happened before was that the rubber tips wore thin from being used
on hikes by the wife. They holed in about a month (often less time than
that). I usually left them on for another few weeks, as they still
afforded some protection to the wood tip end for a while longer, even
when holed.

The metal tip was to prevent wear to the wood, as the stick still works
even as a wooden stick. The problem is that it will crack and break over
time, so, the point was to put the metal to protect the end, and to make
a uniform size for the rubber tip.

At the handle end, would something like a bicycle handlebar grip work?
What about another rubber tip without the metal sleeve?

A bicycle grip might work. The wife changes hand position, so, it's
probably best not to put any grip. The whole point was to enjoy the wood,
but, unfortunately, it cracked from being stored in the house, I guess
(very dry here in California these past few years).