I will be arriving at LHR Sunday 11:35AM with a connecting flight to JNB at 9PM. I am arriving from ORD on AA in Terminal 3 and departing on BA from Terminal 5.

I have access to 2 lounges, Club Aspire and No. One Lounge in Terminal 3 and Aspire, the Lounge in Terminal 5, as well as other Priority Pass lounges in other terminals. I have 2 Priority Pass accounts, by the way - one via AMEX and the other through Chase Sapphire Reserve - if that matters.

My questions are:

I have about 9.5 hours of layover. I am traveling alone and will have checked luggage through and be carrying only a small backpack.

I am going to want to rest/nap, clean up, and eat during the 9 hours. I've decided not to go into London because the time is probably too short to do much. I've been there a number of times and love it, but a 4-5 hour visit isn't really meaningful or enjoyable.

Is there a way to remain in Terminal 3 and make use of the T3 lounges before moving to T5?

If so, any thoughts on a preferred lounge to visit at T3. Do either of these lounges offer showers to arriving passengers? Are food options any better at one or the other? Is one likely to be more crowded than the other (it is a Sunday). I know that there is a supposed 3 hour time limit per lounge, but notes here and elsewhere seem to suggest that it is not always enforced. I can probably go in on one card, leave and then use the other card, if necessary.

Similarly, the Aspire Lounge in T5 is said to be often crowded, without bathrooms, with showers that cost either 10 or 20 GBP, and sometimes have waits. Any thoughts on that lounge?

I have also considered using the Hilton at T4 and taking a day room ($109/84GBP), but it sounds like it is a long walk from T4 in a covered walkway and then getting from T4 to T5 involves 2 train rides and at least 1/2 hour. The Sofitel at T5 is much more expensive for day rooms, and both day rooms want me out at 6pm, which still leaves me with a couple of hours to spend while I am only getting about 4.5 hours of room time - which is not a lot...

Are there lounges at T2 or T4 that make sense to visit?

So, what do you think I should do to best use the time I have at LHR on Sunday, given the parameters I've laid out???

Thanks