He didn't just design them. He built them. An earlier post mentions the museum where they're displayed.
Really? Did you even RTFA?
Then why does the article linked to the slashdot entry state:
As a result, his ideas for his super-accurate pendulum clock were forgotten until the 1970s, when interest in the clockmaker and his remarkable timepieces was re-awakened. The artist and clockmaker, Martin Burgess, – working on attempts to decipher Harrison’s plans – produced two versions of his great clock. It is the second of these, Clock B, that has been the focus of attempts to bring it to its maximum accuracy in the past year. “Essentially we have been fine-tuning the clock so that we can bring it to its full potential and accuracy,” said McEvoy.
The article is about the SUPER-ACCURATE PENDULUM CLOCK, not about this shipworthy chronometers. Sure sounds like Harrison never built his super accurate pendulum clock.
So I decided to do some googling/binging/altavistaing/meh myself and not just take the word of slashdotters like you that post no references... and surprise, surprise, what did I find?!? The answer to my question, which just so happens to contradict your statement... The clock that was tested was built using modern materials, and most likely using modern manufacturing techniques.
According to this article: https://www.theverge.com/2015/...
Martin Burgess, a master clockmaker, used Harrison's mechanism and design along with modern materials like duralumin to construct the Martin Burgess Clock B,
And according to this article on the Greenwich Royal Museum website: http://blogs.rmg.co.uk/longitu...
‘Clock B’ is one of two clocks made from modern materials, chiefly duraluminium and invar, that follow the perceived format laid out in Harrison’s convoluted text: Concerning such mechanism