I have spent many hours crossing various seas in microlights. I had a few things that made me feel less nervous:
Radio.
Locator beacon,
Immersion suit. (you're welcome to borrow mine if you want)
Life raft. (bit heavy maybe!)
Life Jacket.
I too would love to cross the channel by paramotor. Feel free to flame me, but I wouldn't worry too much about the legalities. You have no registration letters but, if you want to be semi-legal, you can file a flight plan with a made up call sign (like 'paramotor1'). Call London information and tell them you're flying from a private field near X and landing at a private field near Y. Stay away from airfields and restricted airspace and nobody is going to bother you. Sure, you might technically be breaking the law, as you do when you go over 70 in your car, but here's the thing I've always found in over 20 years of flying - You can sum it up in a few words - Don't build your part up! - You're a dot in the sky. Nobody really gives a shit about you or what you are doing. Sure, if we all crossed the channel tomorrow, we'd kick up a stink, but hardly anyone does it, so who is going to care? You will probably land in a field near a petrol station, fill your tank and fly back to Kent with nobody any the wiser.
In my experience, on a nice day, there are plenty of sailing boats and cruisers that you could land near to in an emergency.
Good luck! Hope you go for it!
Dave