This is getting very technical but here are my thoughts:
[spoiler](1) We may presume Julia's original 1967 formula would have worked, had Barnabas not forced her to accelerate the treatment.
(2) Lang's 1968 formula did work for a time, but it seems that the "destructive" cell in Barnabas' blood that kept him a vampire (according to Julia's original 1967 analysis) gradually developed immunity to that formula, hence Barn's fixed looks at Vicki's neck (one of my favorite scenes) and the howling of the dogs again.
(3) In 1897, Barnabas is still under Angelique's original curse. Julia is able to cure him with a "new, improved" formula (I still find it difficult to imagine how she was able to synthesize it given 1890s medical technology, especially the very low grade that would have been available in Collinsport). The final injections are administered by Angelique.
(4) In 1970, Barnabas becomes a vampire again, this time because of Jeb's Leviathan curse. That curse seems to have induced an even more virulent state of vampirism; Julia's attempt to cure Barnabas failed, and her formula actually intensified his cravings for blood.[/spoiler]
Beyond that it gets pretty confusing, but I do feel that Julia was in her rights to claim that she had cured Barnabas. It's unclear at the end of the 1840/1971 storyline whether Barn would have reverted to being a vampire again. That was what Sam Hall's notes stated, and I presume that a vampire Barnabas made a more attractive subject for the current comic book project than a cured Barnabas would have done.
G.