why would I NOT worry about the phraseology? I'm a pilot, I'm trying to learn what the CORRECT way to ask for it is. now if if I'm in flight and in a bind, I wouldn't let proper phraseology stop me from straight out asking what I need, but this is a conversation specifically about 'what is the proper phraseology'. so now is the time to 'worry' about it, not when it could get in the way of safety.
You are not worried about the standard phraseology for this request because because you are asking for something that is not standard. None of the suggestions made here involve standard phrasing for a standard request. There might be certain mutually understood local phrases like "We'd like the San Francisco Bay tour" but even then it's just plain old English with simple words. Even ATC uses that when giving instructions that don't have a Handbook reference.
Example 1
Pilot: "We're heading to Mount Hood to fly around it for a while."
ATC: "Roger. Advise when you are ready to head somewhere else."
Example 2. Pilot is going to private airport. ATC is unfamiliar with it.
Pilot: Flight Following to PrivateLife.
ATC: That's not in our database. Can you give us something nearby?"
Pilot: Let's do flight following to [ENROUTEAPT]
Later, approaching [ENROUTEAPT} with, not only a different controller, but a completely different ATC facility.
Pilot: We're not landing at [ENROUTEAPT]. We're going to PrivateLife about 20 NM west. Can you stay with us until we have it in sight?
ATC: Affirmative. Let me know.
Example 3:
ATC: We are going to lose radar contact with you soon. But you can stay with us (for fight following) and make position reports.
How's that for non-standard?
Example 4:
Pilot: We're doing a photo shoot over Broadway and 2nd and would like traffic advisories.
ATC: Squawk...
Other than the names, those are real events. I don't have a safety issue with any of them. Much bigger safety issue is thinking that you can't just use simple English and there =has to-= be a standard phrase for everything.