you ancien LEO, good to see you - our hearts are in the same place.

A bit North of you, we Michiganders have a statute:

THE MICHIGAN PENAL CODE (EXCERPT)
Act 328 of 1931
750.218 False pretenses with intent to defraud; violation; penalty; enhanced sentence based on prior convictions; “false pretense” defined.
....
(9) As used in this section, “false pretense” includes, but is not limited to, a false or fraudulent representation, writing, communication, statement, or message, communicated by any means to another person, that the maker of the representation, writing, communication, statement, or message knows is false or fraudulent. The false pretense may be a representation regarding a past or existing fact or circumstance or a representation regarding the intention to perform a future event or to have a future event performed.
So, what you describe here:

from selil
As such to even merely make claim could be considered a fraudulent act.
as a "fraudulent act", is clearly a "false pretense" as defined by 750.218.

Now, that statute does limit the criminality of "false pretenses" to five general situations ([#]s added to point up elements) :

Sec. 218. (1) A person who, [1] with the intent to defraud or cheat [2] makes or uses a false pretense [3] to do 1 or more of the following, is guilty of a crime punishable as provided in this section:

(a) Cause a person to grant, convey, assign, demise, lease, or mortgage land or an interest in land.

(b) Obtain a person's signature on a forged written instrument.

(c) Obtain from a person any money or personal property or the use of any instrument, facility, article, or other valuable thing or service.

(d) By means of a false weight or measure obtain a larger amount or quantity of property than was bargained for.

(e) By means of a false weight or measure sell or dispose of a smaller amount or quantity of property than was bargained for.
Part (c) [itals] covers a Hillar-type scheme.

The statute as written does not expressly cover some of your examples:

from selil
... monetary or significant compensation including assuaging license fees for vehicles (Pearl Harbor Survivor plates, MIA Plates, Disabled Veteran), increased consideration for employment (veterans preference, Purple Heart awardee).
but a well-inclined judge could fit the statute to the facts if "false pretenses" were used to, say, apply for a license plate. Or, the statute could be amended to add cases to the present five general cases.

But, what if person does not take the step of applying for something. We are then into the law of attempts - not a conspiracy which requires two or more persons.

So, we look to the Michigan statute on attempts (emphasis added):

THE MICHIGAN PENAL CODE (EXCERPT)
Act 328 of 1931
750.92 Attempt to commit crime.

Sec. 92. Attempt to commit crime—Any person who shall attempt to commit an offense prohibited by law, and in such attempt shall do any act towards the commission of such offense, but shall fail in the perpetration, or shall be intercepted or prevented in the execution of the same, when no express provision is made by law for the punishment of such attempt, shall be punished as follows:
.....
[punishments depend on the punishment for the underlying offense]
Certainly wearing the medal, uniform, etc. are acts. An underlying "intent to defraud or cheat" probably would follow or not follow from the context of the act. You don't have to be a lawyer to dream up facts that would or would not make an "act towards" and would or would not be "intent to" in the context of that act. In fact, those issues are typically questions of fact that are decided by juries, not judges.

Thus, as you say, there may be room to shape the "Facts of the Case" and the "Law of the Case".

Regards

Mike