I came back to this problem after giving up a few months ago and am ready to give up again.
On my first effort I followed the instructions in John Goldsmith's blog here
https://blogs.msmvps.com/visio/2005/06/05/custom-line-ends/ it sorta worked, but the line ends ended up being opposite of what was described. Instead of looking like this (----), they look like this )---(
Also implied in these instructions and others, is that you only need to create one line end, if you apply it to both ends of a line then one would come in as a mirror image (mirrored on the vertical plane). On my first attempt with my own line ends I created just one line end and it came out close to what I wanted. One end was mirrored, but was also mirrored on the horizontal plane too which I did not want. The line ends I wanted looked similar to what John had, only with "tails", see
line ends1.vsd. Since one of the line ends was not oriented right I made another try by creating line ends for both ends of the line, one being the mirror image of the other. This came out worse than the first effort. The line end was still mirrored vertically and horizontally compared to the image in the line end definition, see
line ends2.vsd.
And, by the way, it is always the beginning line end that messes up, the end line end always comes out fine. Another thing I discovered while working on this, contrary to what previous instructions say, having guides in the pattern would offset the line end shape from the line and prevented selecting line by anything other than the "ends". DO NOT USE GUIDES in the line end definitions!
So it seems that visio has some type of bias against the beginning line end shape, even if I edit the definition and rotate it in some arbitrary way, it still comes in the same, WRONG!