Scoobster,
As you say you are building hours towards a (presumably EASA) CPL, you should follow the guidance offered by AMC1 to Part FCL - FCL.050 Recording of flight time:
https://easa.europa.eu/system/files/...20Part-FCL.pdf
I've yet to see an FAA 'Airman' log departure and arrival times hence the discussion concerning Local or Zulu/UTC doesn't come into it over there; you should, as recommended, record in Zulu/UTC and so for Florida, its L+5 (which I think you know by now
). As suggested, log as you would at home as Hobbs can present problems (I'm aware of EASA students in the U.S. who have suffered a shortfall in syllabus hours because they logged as their instructors told them (Hobbs) and were therefore approximately 10 mins short for every sortie).
Another peculiarity of the FAA is the allowance of more than one P1 in the event one occupant at the controls is a CFI and the other a certified pilot (assuming both FAA). I take it you must have an FAA Private, in which case that's OK, but not under EASA, so for the 'checkout' it ought to be P/UT. PICUS would be acceptable if your instructor is EASA approved.