UK UK Pilot travelling to Miami, USA

Just show up and say you are filming for pleasure. There's nothing they can do about it.
And , by the way, there is also nothing wrong with telling Customs officials you are "working" in the States as you are doing so for a UK company and the footage will only be seen in the UK. They don't need to know that it might be worldwide, if it is.

I flew in from Toronto to Tampa two weeks ago with my inspire and had no issues whatsoever flying it near the beach in Clearwater. I do have an FAA licence mind you, that I applied for online and received, and I did ask a National Park Patrolman if I could fly and he said no problem.
I didn't fly very high and I didn't fly long. I filmed along the causeway over the water.
Oh, and BTW, again, I carried my 6 Inspire batteries in my laptop case and no problems anywhere.
 
I would go a step further and remove the "for compensation" language. The test is if the flight is for commercial purposes. Real Estate agents are not charging themselves to film their own listings, yet they are not allowed to film from drones since the purpose of the flight is commercial. That's why the idea of shooting for free and then billing heavily for video editing won't cut it either.

You need to find someone who has both the 333 exemption and a qualified PIC to fly. You could find someone who would fly under your direction, and you would operate the camera with a separate controller. Then you would be legal without losing control over the shoot. You would effectively be operating as the DP and/or camera operator.
 

He did find someone with a 333 exemption and a qualified PIC, Me! I researched the location and found that it is within Class B airspace that can not be flown legally. Perhaps an additional COA may have helped but it can take a long time to receive one if at all. I contacted a lot of authorities to try to fly that location and could not get permission. I am not sure if he ever did find someone to do the shoot or just abandoned the aerial portion of the shoot. Maybe the OP will chime in.