Our Dali/Marx work led us initially to The Center of Dalinian Studies... but we may have to keep digging.
Wired Relic Wranglers finally connected with the center. A representative said they currently do not have a research arm able to assist us further with uncovering the lost script. The representative offered a few additional resources on it (and I'm currently confirming that it's not in their possession), but still no definitive location of the actual script.
The Center of Dalinian Studies cited the following three texts as having direct quotations from Giraffes on Horseback Salad:
Obra completa
Dalí. Cultura de masses
Dalí & Film
Two of the titles are available on Google Books (*Dali & Film *is searchable and lists a page with the script mentioned) but none are available for open browsing yet. Time to work on acquiring a copy...
In the meantime, user @stefant of Marx-Brothers.orgshared another publication from 1937 with a feature on the relationship between Dali and The Marx Brothers. While it doesn't include text from the script, *Giraffes on Horseback Salad *is referenced and images that Dali created related to the script (which sat in Harpo's home) are included. See one for yourself below or read the full article for more.