I have done a little more research on this grounding issue, and understand it better now.
Here is what I have learned so far. Please correct me if I am wrong.
There are really two categories of grounding.
The first category is "equipment grounding." In this category, equipment chasis, faceplates, breaker boxes, solar panel racks, exposed metal parts, etc. are connected to earth ground.
This is to prevent the metal parts from becoming electrically charged if a loose wire comes into contact with them, etc That would be dangerous because, if you touched the charged metal, you might provide a better return path for the current (esp. if simeltaneously touching a water faucet, etc.) leading to an electrical shock. It also provides a ground path for lightning strikes, etc.
Almost all systems should have this type of grounding.
The second category is "electrical grounding." In electrical grounding, one side or the other of an electric circuit can be connected to earth ground as well. For example, if the negative terminal of a battery was connected to earth ground, then it would be a "negative ground system," and if the positive side was connected to earth ground, it would be a "positive ground system." With AC current, there is really no difference between the two legs of a circuit. So, calling one "neutral" and one "hot" is merely a matter of convention. And, by this convention, "neutral" is generally connected to earth ground. However, whichever "leg" or "terminal" is connected to earth ground, the other voltage (potential difference between the two legs) is now "referenced" to ground.
For whatever reason, it became customary in the US (and some other places) to tie one leg of power to earth ground (what we call the "neutral" leg).
However, it is possible to have neither leg tied to earth. There are many obvious examples. Your cell phone is not tied to earth ground. Your car is not tied to earth ground, etc.
This is called a "floating ground."
The National Electrical code permits floating ground in certain alternative energy systems for home power, and floating ground systems are considered as safe (or arguably safer) than earth ground systems. However, there are some additional requirements since neither leg is tied to earth. For example, both power legs must be fused or have a breaker and a disconnect.
As discussed above, my specific area of concern is using an automotive style inverter (which is presumably designed for a floating ground) in a home power system.
After more research, I understand the problem somewhat better. A large inverter designed for home use (such as a Magna-SIne), has an isolation transformer in the output stage. In other words, one coil of the transformer is connected to the DC side of the system, and the other coil in the transformer is connected to the AC side of the system. Therefore, there is no hard-wired current path between the DC side and the AC side, and no harm is done is both the DC side and the AC side are referenced to earth ground (or not).
However, with smaller solid state inverters, there is no isolation transformer. The current merely flows through the electronics from the DC to the AC side of the system. Therefore, if the AC side neutral wire is referenced to ground, and the DC side is referenced to ground, then the path through the neutral leg of the inverter can become the "preferred" ground path for currents, thereby frying the delicate electronics.
As Dave said above, the simplest way to cure that potential problem is to dereference the neutral leg from ground on the AC side. Then, there is no possibility of the preferred ground path being through the inverter's electronics (at least under normal conditions).
However, I do wonder if simply dereferencing the DC side of the system from earth ground would not accomplish the same purpose and, if so, that this might be a better solution? After all, you could still maintain chasis grounding on the DC side, and the voltages are lower on the DC side of the system.
Frankly, I don't see a great deal of advantage to not making the entire system a floating ground system (with appropriate chasis grounding) but I may be missing something.
PS: As I have stated before, this is an "experimental system" and I am not concerned with code compliance from a legal perspective. However, I am concerned with safety, and I realize that the Code can be a good guide to safe practices (although there is always more than one way to skin a cat).