You can skip steps 2 and 3 by using https://www.shipsfromandsoldby.com to search or by appending a certain string to the URL which I forget now. I'm not affiliated with that site (and it DOES use affiliate links) but I've found it useful.
Just tried it, doesn't appear to work. It does redirect me to search results on amazon.co.uk, but some of the results are items from third party sellers.
Hmm, I just tried it again and both the first and last page of search results were all shipped and sold by Amazon. My search term was "geiger counter" and results were from amazon.com.