Nearly every camera discussed on this forum will do the job. They all have stabilization, automatic focus and automatic exposure.
Remote control may be the most difficult. I am aware of only one that came with a remote, the TM900. But, it was infra red and might not work in bright sun very well. The current version may have the remote, I'm not sure. The current version is the X900 You can read about it here: http://www.avsforum.com/t/1400074/the-official-panasonic-hc-x900m-owners-thread
. It is currently being replaced by the X920.
If you can figure out how to do without the remote, look at the Sony HX20V or the Panasonic LX-7. http://www.avsforum.com/t/1447996/the-panasonic-lx7-as-a-video-camera-thread
No, they don't look like camcorders but are! I'm too old to water ski anymore, but I have no doubt I would get good results with the HX20V as long as I mounted it where the record button is reachable.http://www.amazon.com/Sony-Cyber-shot-DSC-HX20V-Digital-3-0-inch/dp/B006K551WQ/ref=sr_1_1?s=electronics&ie=UTF8&qid=1362156065&sr=1-1&keywords=hx20vhttp://www.amazon.com/Panasonic-DMC-LX7K-Digital-Intelligent-3-0-inch/dp/B008MB719C/ref=sr_1_1?s=electronics&ie=UTF8&qid=1362156145&sr=1-1&keywords=lx7
The two challenges I see are aiming and vibration.
Aiming: I don't know how high the tower is. Some camcorders and cameras have an articulated LCD monitor, like the 9x0 series above. If you go to that link you can see reference to the 7x0 series that have the same type monitor. The idea is you point the monitor down. It is commonly done at crowded outdoor events. The shooter holds the camera above his head to get over the crowd. Sometimes you see them using a monopod or tripod held above them. I think what I would do, is use a ball head or miniature ball head between the tower and camera to get it pointed right. I think I would try to mount it on the tower above a seat or something so you can reach it. If you don't know it, the thread size is the common hardware store 1/4 x 20. There are also a variety of camera clamps with the screw built in. If it were me, I would mount it low enough on the tower for accessibility, but high enough to be dry.
Vibration: Image stabilization is very good at reducing human induced movement. That is a lot different than boat and engine vibration transmitted through hard mounting on a tower. It may work fine. And, it may work well with it turned off. Because of their light weight, the HX20 and LX-7 may be less vibration prone than heavier cameras. The best results may come from having the (required) observer hand holding the camera. The observer's arm will make a great vibration dampener.
If hand holding becomes the choice, the amazing Sony GW77 is ideal because it is waterproof and takes exceptionally good video. There is a thread here dedicated to that camera.
To summarize, I would try it with the cheaper of the HX20V or LX7, depending on promotions and pricing. Wait to buy it from a reputable source until the weather is good enough to test it. If it does not work to your satisfaction, use the 30 day policy and trade for a GW77. Read here: http://www.avsforum.com/t/1419847/sony-hdr-gw77-waterproof-dustproof-shockproof-small-hd-camcorder
The easy way for batteries is to buy extras and charge them at home. You can get 12 volt chargers fairly easily if that seems more convenient.