You need to inventory those things that are important to leave on while the boat is "in storage". I typically leave mine for the winter, so I need to leave power on to the battery charger and to the bilge pumps. Those are not wired through the inverter. I also leave the water heater on for ER warmth. That is not wired through the inverter. The inverter is part of the charger system, as I have an MS2000, the same as you. On the panel there are 4 green LEDs to tell you at a glance what is on, what is not on. There you can verify that your inverter is NOT ON.
We also have regular and frequent winter power outages at our marina in downtown Vancouver BC. If the inverter was left on, during those power outages, I would be concerned about the FLA house bank being depleted and damaged over the winter.
As for the person regularly "checking on" your boat and its systems, my instructions to that person would be:
1 check the mooring lines and adjust as necessary. Here you really need to know that your "checker person" is competent.
2 operate the bilge pumps on "manual" whenever at the boat.
3 leave bilge pumps in "automatic" mode at all other times.
4 If on manual, there is water in the bilge, call me to discuss.
5 do nothing else.
6 (optional) send me a picture of the Xantrex panel to verify that the inverter is still in the "off" mode.
7 lock up when you leave.
8 verify that you did nothing else.
Diesel engines wear most on cold startup. Unnecessary cold starts will not add any benefit, but will shorten the life of the engine. Having yours started several times over a layup, with you far away and unable to deal with any problems noted, will only add stress to your life. A person unfamiliar with the characteristics of your boat will inevitably find problems where none exist, adding more stress to your remote life.
My mooring lines are set up so that when I enter my shelter, all of the lines are part of the shelter and originate in Non-adjustable, fixed end points. Each of the lines has a spliced loop at the boat end, each which is simply dropped over a cleat. This system allows quickly tying up when arriving at the shelter, with no adjustment of lines, ever. If you are leaving your boat for any extended period, with others likely to move your boat or even merely to adjust your lines because they think they can do a better job than you have done, I suggest changing to a "non adjustable" system. spliced loops on both ends of the line, with the dock end permanently attached, would do the trick. Otherwise you just have to trust that nobody with less than optimal competence will touch yours while you are away.