It’s not necessarily incorrect, but it will probably make you sound antiquated.
Probably the most famous usage of “all the…” with a singular noun comes from an oft-repeated stanza of Shakespeare’s As You Like It, which begins with:
“All the world’s a stage…”
So, is it incorrect? Given that Shakespeare is often credited with helping to standardize the English language as we know it today, and that it was grammatical enough for him (or them—whoever “he” may have been), read and recited by millions of English speakers from the moment it was first inked, I think it almost certainly cannot be judged as “incorrect”.
But does Shakespeare’s use of the phrase compare directly with your phrase “all the trip”? One might be tempted to make the argument that in most cases the phrase “all the world…” is just an archaic/literary/poetic synonym for the word “everyone”, as in “All the world’s gone mad.”, however in Shakespeare’s famous line, that argument does not hold because Shakespeare follows it up with “And all the men and women, meerely Players [sic]”, and replacing “all the world” here with “everyone” would render the two lines nonsensical. So I think it is clear that his use of “all the…” is identical to the example in your question.
However, in using Shakespeare to justify the use of the phrase in question, it is important to remember that he wrote it in the early 17th century, and such a historical example could therefore be considered problematic as a rubric for grammatical modern English. Many other words and constructions Shakespeare uses have long fallen out of regular usage, though this doesn’t necessarily make them ungrammatical. Despite its antiquity, the phrase remains so frequently quoted and familiar to the English-speaking world that I would argue it’s never really fallen out of usage.
Even if I think there is a valid argument vis-à-vis Shakespeare (and usage inspired by his own) against “all the…” with a singular noun being incorrect, I think using it will leave you sounding antiquated, as I mentioned in the first line of my response. The main reason for this is that the only time most people hear or read a phrase like “all the trip” is in the context of the famous line itself. By and large, most people would use “the whole trip…” or “the entire trip…”, and I fear that “all the trip…” is so limited in its use today and so inextricably bound to that famous line that you risk coming across like you’re either deliberately nodding to Shakespeare, trying to express yourself in a florid or overly dramatic or poetic fashion, or as simply antiquated.
So while I don’t think it can be argued that “all the…” with a singular noun is “incorrect”, I would caution against its use as simply inadvisable, and stick to “the whole trip…” or “the entire trip…”.