I realised this a couple of years ago in Memphis (of all places!). We booked a tour of Elvis' house and in the middle of the day the house was packed with tourists. Later the same week we booked a tour at four (it closes at six). There was no fucker in the house at all except the guides, who didn't give a fiddler's fart and were happy chatting because it was the end of the day! We spent ages in the jungle room etc. . it was great!
When I went to Maes Howe it was early afternoon, and it was packed. I had to wait till people left before I got chance to check the runes etc.
Untill recently there were no ropes around the center of Maes Howe (meaning you can't touch the walls or climb in the other sections). I'd bet if you took a later tour, got chatting to the guide, he'd let you do all sorts he wouldn't allow a crowd to do (ooer!).
Another tip, for what it's worth. Don't bother too much about 'list ticking'. Rather spend time just taking in the 'sacred landscape', as Moth said, from Deepdale, and from Maes Howe, it's all open and fantastic. Walk from Steness to Brodgar (there used to be an avenue there, you can still see a couple of stones in a garden and of course the Watchstone).
There's an excellent bit about the landscape and missing 'Odin stone' in The first bit of the Megalithic European by the way.
Another tip, buy some lovely cheese and wine from Kirkwall, catch the bus to Stromness and have a slap up meal at Julia's Bistro in Stromness. Skip the dessert, and catch the bus (right outside Julias) and take your cheese and wine to the Stones Of Stenness (the bus stops very near). If you're lucky, you'll get a nice sunset and it'll feel like nowhere else on earth.
I'm SO envious. Have a great time!