If you're only interested in taking up a half day. The easiest and probably best option would be to put in at the mouth of the Santa Elena canyon, paddle upstream stream a few hours then paddle back. This option let you control the time and eliminates any time wasted in shuttles and complicated logistics. Best bang for your buck in terms of time. I believe several outfitters offer a canoe drop off and pickup for this exact type half day rental. This trip would put you right in the heart of some of the deepest canyon walls the park has to offer.
However still the call outfitters as current flows will dictate what will work with your timeline and interests. They maybe be able to recommend or put together something else that matches what you want to do.