Welcome aboard, Al-Hakiim von Grof !
You've hit on a fascinating topic. It seems undeniable to me that Jefferson's Epicurean leanings influenced his political thought. However, the final draft of the Declaration went through a committee as well as revisions from the whole Congress before being accepted. A large part of Jefferson's original draft remained intact through the process, but there were significant changes made nonetheless. Here's a history of the creation of the Declaration from the US National Archives:
There's also this from Monticello stating that "pursuit of happiness" could have clearly been influenced by George Mason's "Virginia Declaration of Rights"
There's also
Historian Peter Moore appears to have written an entire book on "Life, Liberty, and the Pursuit of Happiness"
So, Jefferson's phrase doesn't appear to be unique to him or *wholly* a result of his personal Epicureanism, but Epicurus's ideas were percolating throughout the Enlightenment era.
Personally, I'm torn on how I feel about Jefferson. He was a fascinating man of science and invention, a pivotal Founder, a heckuva writer, but many of his actions make him difficult to like and from many accounts he was not an inspiring speaker.
That's probably a more lengthy response than you wanted! I'm glad you found our little Garden here online.