How can I extend the ten minute video limit on a Canon PowerShot ELPH 300 HS? This question addresses the fact that DSLRs have limits on video recording time and provides some speculation as to why the limit exists. It mentions that Canon has a 30 minute limit.

I am recording HD video on a Canon PowerShot ELPH 300 HS point-and-shoot, and am coming up against a 10 minute limit. This site says that there is a 60 minute limit on standard definition and 10 minute limit on high definition. With 720p a 10 minute video is about 1.5 Gb. I wanted to mention the 10 minute limit explicitly because it seems that many people talk about a 30 minute limit and so this seemed like a somewhat unique case.

My question is whether there is a way to extend the limit from 10 to something like 30 minutes? 10 minutes is just short for my purposes of recording my own judo tournament matches.

I guess it would have to be some kind of patch to the firmware. Does such a thing exist?
I believe the limit is due to the file size, not the actual recording length.  This forum thread seems to confirm this for the T2i/500D, and Wikipedia agrees for the 5D mkII.  Also according to these sources, the limit for both cameras is 4gb.

For the PowerShot cameras, the file size limit is likely much lower. For the S2, it appears to be 1gb.

What all this means is that the time limit isn't a time limit, per se... but a file size limit.  So if you are able/willing to reduce the file quality, you may be able to extend the time limit.

If you can shoot in a lower quality video mode (say 480i instead of 720p), that will likely improve your recording time.  If you can reduce the frame rate, that may improve your time limit, as well.  Of course all of these things will make the video noticibly lower quality, as well.

If you can't get different equipment, you may be best off strategically stopping and starting the video during pauses in the action.