Frisbees are great, we have one that is made of material that isn't hard on he mouth has a firm rather than hard edge, quite flexible. I think I got it through the K9 online shop. We also have a $5 ball from KMart that she will endlessly play soccer with ( best with us involved of course) Maggie at Gracies age loved killing plastic buckets and brooms, hours of fun. As she has got strong jaws and teeth now the buckets last less than a day so we stopped them, she still throws her brushes around the back yard though.
It has been raining alot here lately so soccer and frisbee out the back have been the only way we could esxercise her between showers. The unpredictability of the frisbee taxes her brain more than the ball I think.
Also it is often stated here that any form of obedience/fun training will tire her by taxing their brain.
As she made it over 12 months she is starting to settle. We did manymany sessions waiting for her to settle/come/ damn well do what she was told...lol
Keeping a smile and sounding pleased when she finally arrived was very taxing. The beach experience was similar to your dog park, ended up getting there at sunrise to limit the problems.