Amphibious Atlantic Cruiser

Those wheeled Vehicles pictured look like they require a boat ramp or hard pack flattish surface without obstacles to keep from getting bogged down on the land part of amphibian..

 

Maybe the simplest thing to do would be to take a small lightweight self righting boat, that could carry a take-apart chassis, with a way to feed power to the wheels of that chassis. Or if it was really small, you could pull the boat yourself, or use solar powered motors. But the boat would really get tossed about by big waves.

You could read about Freya Hoffmeister's ocean journeys. She has taken a sea kayak solo through some of the most difficult and dangerous seas. You could possibly fit a take apart trailer inside a sea kayak. I don't think her boat was self righting - she is a very skilled boater, who undoubtedly knew how to roll her boat upright, and a lot of people think she takes very big risks. To paddle around the world (or perhaps to add a small sail, and use the "prevailing" winds, or a solar powered motor), would take a very long time.

That's a problem with a lot of possible solutions. At mid-latitudes, around the world is a very long distance. If you don't go fast, it might take many years. And you need lots of food and provisions along the way. (There are lots of times and places you won't find many fish.) And the slower you go, the more likely you are to encounter a lethal storm.

Passage distances could be shorter at high latitudes, but the weather could be a major problem. Around Antarctica, you would be extremely likely to encounter breaking waves large enough that falling off the top of the waves to the trough, or having the wave break on top of you, might kill you. I was somewhat involved some years ago with an experimental platform that measured waveheights in the southern ocean, near Australia and Antartica. They routinely saw waves over 40'. A quick web search finds pictures of big waves at places like

awesomeocean.com/guest-columns/southern-ocean-terrifyingly-huge-wave

www.saildrone.com/news/wave-height-southern-ocean

pursuit.unimelb.edu.au/articles/exploring-the-birthplace-of-monster-waves (which mentioned 30 meter rogue waves).

They look intimidating.

You probably won't see waves quite that large near the north polar ice cap - but you might not get a clear passage, and the sea there is shallow in places. You may also sometimes have to fight tidal races that exceed the speeds attainable by most small boats. I'm not sure you can avoid going into or near Russian waters. Not many non-Russians would be welcome right now in or near Russian waters, even if you asked for permission. And Russians wouldn't be welcome right now around most of Europe and the much of the Americas.

In addition to large waves, you need to worry about high winds. Hurricanes, typhoons, etc., have become increasingly common of late.

In short, unless you have a serious ocean going ship that is made for the weather - and maybe even then - you likely have a low chance of living through your adventure.

 

Life threatening wind, waves, and storms deserve special consideration, as any kind of rescue may not come soon enough. Methinks the amphibian craft's design should involve some form of submersibility to provide a quick escape by going below such hazards, but short of being a fully functional submarine. Some of the smallest ones might have been the Civil War submarines, which did not fare well. Of course, using something that goes below the surface introduces additional hazards in itself.

Here's a small prototype,

https://www.guinnessworldrecords.com/world-records/smallest-submarine

I believe there's even smaller versions that involve using separate scuba gear in the human power submarine competitions, but I don't know if any of these could stay down long enough to get through the rough patches?

 

those clam buggies seem to be rolling on extremely well packed sand.

flats of SF Bay you'll sink up to your armpits the second you step in and thats no joke. Saw a small hovercraft rescue team practicing which makes sense because the only other thing that could get to someone on the flats would be a helicopter. Was out kayaking and a windsurfer dude was hitting mud and semi-stuck with tide going out with sun going down and he was worried and for good reason.

 

I could see how a self-contained amphibious vehicle like that would be kind of fun. A kind of go anywhere vehicle - sort of.

But the ones like in those videos look horrendously inefficient, on both land and water. I bet they don't get a lot of miles / gallon (or km / liter). Perhaps, to an extent, making something streamlined in both environments, is kind of hard. Anything with wheel wells in the water is going to create a lot of drag. And if the wheels are on something that folds up and sticks up into the air, that's a lot of drag in the air, when you are on land.

In a sense, designing a vessel to do this might be an interesting and challenging engineering problem. Would there be a way to make it fairly efficient? And still be pilotable by a single person, if that is the goal?

Of course, it is probably more practical and economical for ships to send a small craft (or "tender") to shore, which in turn carries a small land craft, like a folding bicycle or eBike. Or maybe a small amphibious vehicle? But if the o.p. wants to be the first to do something, that wouldn't qualify.

I have known kayakers who did "first runs" of whitewater rivers, so they get in the record books that way. Some of them are sponsored boaters, who make a living by doing crazy, dangerous things. And kayakers like Frea Hoffmeister, some of whom are also sponsored, do "firsts" too. (There are a number of other expedition kayakers who have done firsts too.) There are many people in the sailing community who have done firsts too, and some still are doing them.

But I think all those people were very experienced, with a lot of skill.