I agree with Skip to get the "official" word but my take is that there are two main considerations - Customs and Immigration.
The boat is already in the US and presumably you properly registered it and paid sales taxes
(if any). Sales tax is different than customs, which is about importing items. So customs is about the boat and equipment
Immigration is about the people. You presumably cleared immigration at your point of entry and I presume you flew in. I also presume anything you hand carried personally (items) has been properly cleared through customs at the airport
So my opinion is you are fine. It would be as if you flew in and rented a charter
boat. In this case you just happen to be the owner of a vessel already in the USA.
I am not sure what happens when a Norwegian clears a US boat (customs) that he/she owns out of the USA and clears it into another country but I don't think it is a drama.
I am a US citizen and own a Singapore
flagged vessel. I have been in and out of Indonesia
numerous times and there is absolutely no issue.
Just remember immigration is about the people - and we have had lots of drama here as we often have 4-5 nationalities on board with differing visa requirements - and customs is about the stuff.
The "Q" flag is only a slightly confusing aspect. You need to understand the rules of the port you are entering on when and why to fly the Q flag but in general it will be flown until the boat (customs) and crew (immigration) has been cleared.
Where and how you can cruise
within that country can also have some twists. Technically foreign boats in Singapore
have to file a float plan when changing marinas
. I know a few boats "based" here with foreign flag and they don't seem to file float plans.
Noonsite is a great resource for researching exits and entries from port to port. Followed up with questions here to see if anyone has actually done your specific example.