OK, I used Drax tool to add the Vegas Pro (v15 in my case) Markers to the Vegas Pro rendered AVC encoded MP4 file. Below are a modified set of instructions to do this based on a 2009 thread. (the Vegas steps were augmented slightly)

IN VEGAS:

1.       Render your file to AVC encoded output (using MAGIX or Sony AVC templates), and rename the .mp4 extension to .m4v (important).

2.       With your Vegas project open, make sure to set the project’s Time Ruler format to "Time" (not “Time & frames” or one of the other timeline formats). Go to File->Properties->Ruler for this setting

3.       Open Edit Details (View->Window->Show Edit Details).

4.       Choose Markers / All Fields.

5.       Click the upper left box to select the whole table. Ctrl->C to copy the marker data.

6.       Open a new Text file on your desktop. Paste the marker data into the file. Save the text file ("Chapters.txt" for example).

7.       Edit the saved text file, deleting the column heading (first line in file) and add a new first line that contains “00:00:00.000                   Begin” (or use another chapter name of your choosing besides “Begin”) -- Drax seems to want the first chapter marker in the import file to be at "“00:00:00.000"

IN DRAX:

1.       Open your renamed .m4v file.

2.       Click on the "Chapters" tab at the bottom of the window.

3.       Go to File->Import Chapters

4.       Click on your newly-created "chapters.txt" file (you can also edit or add chapters manually if wanted).

5. When the new chapters have imported successfully, click File->Save.

So now when I open the Drax modified M4V-wrapped AVC file the "Next Chapter" button in VLC media player advanced to the next Vegas created marker (same should happen with other media players)