To reinforce what Marco said, you definitely have the eye for composition etc so just aim to build on that as you're already off to a solid start!
If you were looking for a starting point to start shortening the reel or to give purpose to each group of shots, maybe consider breaking each of the points you noted into shorter individual pieces that show examples of each of the titles.
For example, "Your traditions" - Pick your best and most impactful shots/pieces to showcase that. "Your eccentricities" Again, pick the best and put them into a video that speaks to that heading.
Shortening the videos means you have less time to make an impact so, it'll drive you to pick the shots that will make the most impact right away!
Also, trimming them down helps people find examples relevant to their projects they'll want to hire you for as they wont have to sit through a much longer version and hope that you can deliver what they're looking for. It also helps for blogrolls, website, social media etc as you can deliver a stream of shorter videos instead of blowing the proverbial load with one longer edit.
Did that make sense? Hope it's not too much of a ramble!
Good luck and keep going!
I agree that using a competent swimmer is a good idea and/or to ensure that whoever you are using (character, stunts or accomplished swimmer) is comfortable and able to swim in wardrobe. The hidden safety line is a good idea, but i'd run wardrobe tests in a pool with whoever will be performing this stunt to get a solid understanding of how these factors affect swimming abilities. Also, you need to take into account that this performance will change with water temperature too so just because they can do it in a pool doesn't guarantee the same results in an icy cold river.
I would also caution against the use of hand warmers inside a wetsuit. Many of them get pretty hot and can actually burn skin if placed in direct contact. They even warn against this on the product packaging as they're usually designed to work inside clothes. Also, they work in reaction to air so i'm not sure of their efficacy once submerged in water.
I also recommend that you have a warm place to quickly get the actor to once they have done the swim. Be it a fire, vehicle or tent etc. as hypothermia and other resultant conditions can present themselves quickly. I'd maybe encourage whoever you use, to get a physical done prior to the stunt too. People with unknown heart conditions etc can quickly experience cardiac problems when subjected to the shock of cold water.
I'll let you know if i think of anything else. I've been contemplating a similar idea for a screenplay im writing which involves a scene in the Ocean so it's a regular thought process for me at the moment!
Good luck and keep discussing your ideas for this scene as you may come up with solutions & ideas you didnt first anticipate!