I'm sure each person will approach it differently. The law says that you have to give name and date of birth if you're being issued a summons per Title 17-A Sec 15-A. When operating a motor vehicle, you must produce your driver's license on demand of a law enforcement officer per Title 29-A Sec 1408. There's another law about producing ID if you're in a drinking establishment and suspected of being underage that doesn't really apply here.
My personal practice when I am demanded to identify is to ask what crime I'm suspected of committing. If they can't come up with anything criminal I'm suspected of, I'm not giving my ID. "suspicious activity" is not a crime. "you're carrying a gun" is not a crime. "I think you're going to rob that convenience store" is a crime.
There are many applicable Supreme Court decisions to fall back on that are discussed in the other thread you linked.
Terry v Ohio - They need reasonable suspicion of criminal activity to detain you.
Delaware v Prouse - They can't just stop random people to check ID.
Hiibel v Nevada - Laws that require identification are legal as long as they require a reasonable suspicion of criminal activity.
DeBerry v US - The presence of a firearm where it is otherwise legal, is not reasonable suspicion of criminal activity.
Kolender v Lawson - Laws requiring identification of loiterers or wanderers absent suspicion of crime are not Constitutional.
My reasoning for not identifying myself to police if the law does not require identification is quite simple. When you identify yourself, your name goes into a report of the incident. That report is a matter of public record. Many newspapers publish complete police logs on their website. Websites are searchable. If I've done nothing illegal, I don't want my name coming back to a police report about a possible weapons incident. Most employers perform background checks on potential employees and this could disqualify you if you're looking at two equally qualified candidates, one who has a clean BG check and one who has a police report about guns.