After a reasonable amount of time with the lovely FT search facility, I think I have this figured out, but please correct me where wrong!

Scenario

Passenger elite status: AA Platinum, OW Sapphire
Class of travel: Oneworld F award ticket, arrive ORD-LHR T3 on AA F, dep LHR-CCU T4 on BA J (no F on 3-class 777 to CCU)
Available transit time: 5 hours

Question: What access available to fast track, MB spa, showers, and lounges?

Answer

T3 -> T4 transit airside Fast track available through FCC security.
Reasons: BA J outbound boarding pass (usually works), AA F arrival (occasionally works), OW Sapphire (rarely works).

T3 -> T4 transit landside Due to 5 hour transit, should not be necessary, except if outrageous congestion at FCC.
- Fast track through T3 immigrations: available due to premium AA arrival
- fast track at T4 security: available due to premium BA departure

MB Spa and Showers (T4 Gate 10) available due to BA J outbound. Massage/spa appointments spotty. MB showers always available. Better than showers at Gate 1 lounge.

T4 Lounges Unclear if "J BP, but on F ticket" entitles one to First lounge. The point appears moot, as the consensus appears to be that T4 First and Concorde lounges are chronically (over)full with ossified specimens. Consensus appears to be to use the Gate 1 (aka Pier 1) lounge, which is accessible both due to J class outbound, as well as OW Sapphire. One guest permitted.

T3 Arrival Lounge If considering the landside transit option, AA arrival lounge available. No real reason to use - better to transfer to T4 and use MB shower/spa and Gate 1 Lounge.

So, how did I do?