Hey so that mission had a couple mistakes, which I assume were just oversights because you remade it quickly to remove the mod dependencies, but I'll just point them out. For one, it had no playable unit. The only unit you placed was set to "playable" and not "player" so playing it how you had it, you spawn in as splendid cam lol. No worries. You also set the BLU objective marker as just a small marker over the sea. This shoots an error obviously, because there are no military objectives over the sea.
Here is a version where I fixed that for you, and for me, when launching in local MP, this saves and loads (it is persisting player position, time of day, etc, all is good doing a quick test).
https://www.dropbox.com/s/ljsku4gg99az88u/OPERATION_WHISKEY_TEST.Tanoa.zip?dl=0
What's odd is, if I save it in local MP, then run it again in local MP, it persists just fine. But, if I save it in local MP, then load it in SP, although I get the message my mission state is loading, it doesn't seem to. Not sure what's going on there (might be an internal bug? Might work this way on purpose, not sure), but as long as you keep the mission in local MP, it should save and load. At least how I have it.
Try again and let me know.