sechel,
The paste in the Hebrew was taken literally out of the sicha which is posted online. https://www.chabad .org/therebbe/article_cdo/aid/2988061/jewish/page.htm
As for a source, see vikuach haramban: https://hebrewbooks.org/22088 p.34 (page 35 of the PDF), the large paragraph starting in the middle of the page. If you read it carefully, then you understand that his entire argument is based on this idea that moshiach can’t be J-s because he died and the world is still not peaceful, etc.
As for your argument that this can’t be a source because it is a discussion because it’s a discussion with the goyyim, this would be true if it were second-hand. But when the Ramban published it himself in לה”ק, he made it into a valid source.