I think in reality we are more likely to see the kind of act that do the summer evening concert circuits. AT isn't able to provide enough capacity and infrastructure on park for the stadium acts, and tempting / affording groups to do this kind of event as a one off is much harder than if they are on a tour of Summer Concert events.
The Forestry Commission are one producer of these events, running different gig locations throughout the country, normally rotating the same acts around all of them. Their lineup this year includes Plan B, Will Young, The Wanted, Razorlight, Steps, Alfie Boe, Ed Sheeran, Madness, The Wombats, and The Darkness.
Other producers will offer a variety of shows over a weekend, such as a Classical Orchestra / three tennors style gig on the Friday night, a Pop act on the Saturday, and a 70s / 80s / 90s act on the Sunday. I think the idea of running three slightly different gigs on consecutive nights would work well for AT, with the costs of the infrastructure being spread over three events for a short time period, the ability to market a "season ticket" for all the concerts, and the option of doing hotel packages for the weekends etc.
The other thing that some producers are trying is bringing west end type shows to outdoor concerts. We recently did a performance of Thriller Live! at Audley End as part of their summer concert weekend which went down really well. (see below!)