Six hours in London

The Oyster Card is the best card.

The Oyster Card can be purchased at Heathrow, but I cannot remember the exact location. I remember it wasn't hard to find the London Underground desk. You can also purchased the card through a machine.

The tube station is where the signs tell you to go to The Underground.

No matter how many times you use the tube (or buses) during the day, and whatever means you choose to pay (Oyster/contactless etc) there is a fare cap of £14.90 (an anytime cap so regardless of peak or off peak) for Zones 1 to 6 (Zone 1 is Central London, Zone 6 includes Heathrow).
That is as much as you will pay per person.
That is less than the cost of a One Day Travelcard for Zones 1 to 6.

If you have a contactless/tap and pay card, you don’t need to buy any kind of pass - just tap it on the yellow pad at the start and end of every tube trip. It will automatically calculate the best possible price.

Is the 6 hours from 8.30 a fixed time to pick up your hire car that you have to be at the depot by? If so bear in mind that it’s about an hour or more each way to get from LHR to central London depending where you go and that the car hire depots are generally a courtesy bus ride from LHR. Also you need to add on time to get from the plane landing through immigration and maybe collecting checked bags. So don’t expect to have much time. And what will you do with your bags?

Use a contactless card - even with fees that will be cheaper than spending £7 on an Oyster

You may well have, but it's only six hours in London if you have 11 hours between flights

The piccadilly line takes nearly an hour to get into London.

Instead take the Elizabeth Line from Terminal 5 to Paddington Station. About 30 minutes. Pay £’s for an oyster card ( kiosks at LHR) or just use your preferred travel tap debit/credit card.

From Paddington take the Circle Line train to Westminster Station. 20 minute ride. Exit and follow signage to Parliament Square. Believe exit 4 takes you out to the Thames River path and if you turn right and look up you’ll see Elizabeth’s Tower. If you there on the hour you’ll hear Big Ben toll. Climb up the stairs.

Walk around Parliament Square. If you want to see the interior of Westminster Abbey you’ll need a costly ticket.

From Parliament Square walk up Bird Cage Walk (adjacent) to Saint James Park to Buckingham Palace. From there cross Green Park and walk along Piccadilly. Pop into Harrods and visit the food halls. Follow Piccadilly to Trafalgar Square, then turn down White Hall back to Parliament Square. Take the tube back to Paddington. Elizabeth Line to Heathrow.

Like others said, no need for a pass or ticket. Use contactless, either a credit card, phone, or watch; tap into the tube at the turnstile, tap out when you get off. You each will need a credit card or device, see https://contactless.tfl.gov.uk/ for details.

As for your plan, you really do not need to use the tube that much, you just will spend too much time sitting or standing in an underground carriage. I take it you will not actually visit any sights by entering, so I would suggest the following.

From Heathrow, catch the underground (Piccadilly Line) into London. At the Hammersmith stop, get off, walk a few feet across the platform and catch the next District line train. Get off at Westminster stop, follow the signs to the Westminster exit, and you will emerge in the shadow of Big Ben. From there, you can gawk at the Houses of Parliament and over to the Westminster Abbey. Either buy the book or look for the audio version, but Rick Steves has a Westminster Walk that will take you around that area, up Whitehall, to Trafalgar Square.

From there, you can wander to Covent Garden, down to the Strand, and along to St. Paul's Cathedral. From there, go across the Millennium Bridge to Southwark, and wander by the Globe, Drakes Golden Hind, and up to Borough Market (depending on the day, there could be lots of snacks to eat). From there, you could hop back onto the tube, or head to the river and walk it back down to the Westminster Station. You could also head further down river and catch the Tower Bridge and Tower of London.

At any point, you can find a station and head back. There are loads of pubs along the way (I usually stop at several). There are also a few other walking tours in Rick's book that covers some of the areas (St. Paul's area, the Strand, Southwark) so you can piece together a nice (but maybe long) walk that covers all of the essentials of Central London. Perfect for jetlag, and giving you a nice overview of London.