I'll take a different tack - While its hard to say that the dangers of hypothermia are over exagerrated - I'll say that it is, to some extent overexagerated (is that a word?)  If you have some common sense, you probably aren't going to die instantly just cause you flipped over in cold water.

My cousin and I once flipped a canoe over in April, on a NY river that was essentially snowmelt - still had small chunks of ice floating down.
It was so cold, the "gasp reflex" was working pretty strongly and it was hard to catch my breath.  That's when the "common sense reflex" kicked in.  The river was maybe a quarter mile wide with strong pushy current - no way we were going to last long if we tried to stay with the canoe, so I told my cousin to abandon the boat and swim for shore, which we did - we made it to shore after  15? minutes or so? - floated at least a mile down the river - except that we didn't float, but rather we swam as strongly as we could for the bank, doing so with numb hands and feet and legs, but keeping the blood circulating.  When we got on shore, my cousin was pooped out, but I made him run with me downstream to try and catch up with the canoe - so we kept moving, running on lead feet with no feeling for a mile.  Air temp was probably in th fifties with a light breeze? I doubt it was sixty, and could have been in the forties - don't remember exactly.

My Dad and sister were in another canoe following us, saw us go over and with that warning, knelt and made it thru the rough spot.  They followed up our canoe and caught it washed up on a gravel bar, empited it and towed it across to us.  All the time we waited, we kept doing jumping jacks or whatever to keep the blood moving.

It was a spur of the moment trip, and we weren't very well prepared - no spare clothes.  I was going to start a fire, but the matches I had in my pocket in a zip-lock had goten wet - I was the only one with any matches.  We dried off a little, swappped around some dry shirts among us, and proceed to paddle as fast as we could downriver a few miles to the car.

So my cousin wound up catching a cold due to our swim - I was fine, not even a cold.  We didn't die - we didn't get hypothermic even - shivers yes, incoherant no (well no more than on a normal day for me).

So my point is, you have to keep your head and use it, if you give up, well, you probably will die - if you keep moving, you may not even get a cold.

I actually stupidly  fell out of my canoe on one solo trip in Quetico - end of May, not far off the Nym dock.  2 busloads of kids came down to the dock, dumping packs and gear everywhere, burying my stuff.  My only option was to get off the dock asap - so I threw my stuff in my boat and took off.  Trying to paddle and reorganize at the same time, I twisted the bent-shaft paddle around and doing a stern draw or something (wasn't paying any attention to my padling), totally unexpectedly I just pulled myself out of the canoe somehow - boat took on a little water, but stayed upright - so I just grabbed the painter and swam for shore, maybe a hundred yards or so.  It was a sunny day, but early in the morning in May so it was probably about 50?

I just dried off a little, squeezed some water out of my clothes, put on a fleece jacket, dumped the water from the baot and continued on.

You asked about September - my opinion, Sept or Oct, the water is still warm - and likely it will be warmer than the air - I wouldn't be too worried about stayiing in the water a while in Sept, and swimming a boat to shore.  You would have to be moving fast when you did get out though, as the cooler air temp and wind would get you then.  Just change into your dry clothes, and never stop moving till you warm up.

With two canoes, I'd go ahead and try a canoe over canoe if the gear wasn't in the way - most boats I see out there though , they have packs sticking way up above the gunnels, likely enough to get in the way of a canoe over canoe - in htat case, probably best to tow the swimmers and boat to the nearest shore.

I've gone over WW canoeing several times here in Colorado - some of them were in April - the water is cold - a couple times, I didn't have a dry suit on, and it was icy, but I got to shore and chnaged clothes if needed - mostly, I just catch my breath, maybe change into some dry gloves and fleece jacket, and jump back in the boat - keep paddling to stay warm - even wiht numb hands and feet, you can generate enough  body heat to keep your core warm.

Now, I'm not saying you should ignore the dangers of hypthermia - I'm just saying that if you keep moving and use your head, your not all that likely to get hypothermic, even in cold water.  

Seems to me I've been colder on windy rainy days - even with good rain gear, seems like I eventually will get wet, what with water dripping down the sleeves.  My response is pretty much the same - keep moving to keep warm(er) - I always wet-foot, so even in May, my feet are going to be wet - sometimes, wet and numb - I just deal with it.  AND, I do almost always wear my PFD - I wouldn't have survied most of my swims without one!