With 9hrs I'd pop into London for 4hrs for lunch, some tourism, or something like that, then avoid rush hour times and get back to the airport at t-3hrs to enjoy a lounge as it's designed to be. 9hrs would be fatiguing - I've done it one time, fully with the intent of sleeping on the sofas around the corner (after landing from Chile (13hr flight) and flying from London to JFK 9hrs later (another 7hrs!)).
The destinations are more valuable than the lounges. Besides, you'll get to do the lot!
Enjoy