Connecting at JFK DL/VS

does anyone have experience of connecting internationally between DL / VS at JFK T4?

Flying from Caribbean to JFK on DL and then JFK to LHR on VS , same ticket, have about 3h between the two. JFK LHR will be in Upper too.

Am I correct in saying I will need to go through customs / immigration, then collect baggage, then head to Virgin to check bags in again?

Seeing as I am in Upper I guess it would be best to head to the Delta One area once I exit so I can get private security and check in / bag drop there for VS flight? Is it easy to access once you exit arrivals - do you head back up to departures or is it elsewhere?

Any other advice would be appreciated, hopefully there's enough time!

thanks