I am rather more optimistic about the possibilities than some others might be. From the perspective of historical scholarship, keep in mind that the traditional view of the Hellenistic era was (very simply and bluntly put): the classical era of city-state Hellenism was a golden age, the Roman empire was great, too... and that stuff in between couldn't compare. It's just like the myth of the "dark ages" (you know, "everything from 500 to 1500 was grim and terrible and everyone was a stupid religious zealot who thought the world was flat"). Although there have always been more nuanced views, this basic premise about the Hellenistic era was just
wrong. More recently, a revisionist view has emerged, which actually contends that the Hellenistic age was a time of great scholarship and scientific theory. The most prominent of these revisionists is perhaps Lucio Russo-- who is also one of its most radical claimants. We'll get back to his work and views in a bit.
Essentially, what
@LSCatilina wrote about rulers and even scholars not primarily caring about the practical application of their often purely theoretical work is true... but this was a general problem in Hellenic culture. And yes, indeed, "wise men" were mostly philosophers, rather than men of the "hard sciences". The Greek approach to philosophy exactled the "pure", theoretical model, and to some extent looked down on practical inventions. That was for mere artisans, not for philosophers!
But... that tendency, while present, didn't stop philosophers from being practical. It depended on the philosophy. Compare Plato to Aristotle: when trying to define the ideal constitution, Plato started with vague, otherworldly ideals, and tried to put those into a constitution. Aristotle gathered as many constitutions from various places as he could, and compared them on their various merits and drawbacks. Aristotle was also a proto-biologist etc. So certainly some thinkers were more practical than others.
The thing is that the more practical side of things actually flourished in the Hellenistic age. The charge of "impracticality" that was true for the classical age of city-state Greece was actually
less applicable to the Hellenistic era! People like to say "Oh, that steam engine of Heron's was just a demonstration model. Barely a toy, really!" -- but that's hardly fair. The first steam engine invented in the modern age was also not a practical machine yet. It took time to develop it to become practically useful. And Heron was born at the very
end of the Hellenistic era, not at the
start of a scientific age.
This is where Lucio Russo comes in. His theory - which he underpins with very convincing arguments and examples - shows that a lot of knowledge was lost when the Hellenistic states collapsed. Romen commentaries on Hellenistic works on mathetematics demonstrate (to modern readers) that the Romans didn't actually understand the complex math in those works, while the Hellenistic mathetaticians clearly knew what they were doing. That knowledge was lost. So the classical view that the Hellenistic era was a dark age is wrong, and must be turned upside down. From a scientific point of view, the Hellenistic era was the golden age, and much was lost thereafter. To be fair: Russo often goes too far. He proves that the Hellenistic wotld had theory X and technology Y, and then he points to some vaguely-phrased sources and interprets them to mean that "they probably combined X and Y and thus also had Z"! This is very important to keep in mind when reading his work: whenever he provides concrete proof, he's great. When he starts speculating, it's better to err on the side of skepticism, and assume they
didn't have that particular theory/knowledge/technique/technology yet.
But they did have a lot, already. A society that only used pure theory and spurned practical application would not write volumes on how to create a hydraulic pump, nor would it actually use a hydraulic pump to send freshwater uphill trough pipes. But Pergamon had that pump, and had those pipes. And other places uses similar systems.
Now it is true that the Romans were certainly
more bent on practical applications than the Hellenes, typically. But as already pointed out, the Romans did a lot poorer when it came to the underlying theory. So all in all, the Hellenistic era was already moving away from the "lofty philosopher"-mindset of city-state Greece. It's just that the Hellenistic era ended too soon to complete that evolution, and the successors (Rome and Persia) were less inclined to value the more theoretical scientific knowledge of the Hellenistic era.
So, if a way can be found to ensure that more cities have a great library, or a Mouseion, or any sort of centre of knowledge and learning, that certainly helps. The more knowledge is spread, the greater the chance becomes that somone will take the teory and apply it to some practical use. The less spread-out and available knowledge is, the greater the chance that a person who might have a practical use for a theoretical model just never comes across the theoretical work in the first place.
As for the durability of these centres of learning: these were, to some extent, prestige projects. I say so what? Stanford University and the Carnegie libraries were also prestige projects, but that didn't stop them from being useful or from being
lasting. Times of economic downturn (or other types of crises) would certainly affect such centres of learning, but would it make them disappear? No. It didn't in OTL. There would be lean years, and after that, there would be fat years again. That's the way it's always been.
I firmly believe that the Hellenistic era was - by far - the best shot the ancient world had at fostering something like a scientific revolution. Let's say I'm with optimistic Russo about two thirds of the way. It woudn't be "ancient industrialisation", but it would be the kind of development that
could bring future industrialisation far closer. More numerous development of centres of knowledge and learning would be crucial.
However... the political failings of the Hellenistic Era are not solved by this. So I suspect the era would still end, and much knowledge would still be lost. We can only hope that with more centres of science existing, more knowledge would be preserved in the post-Hellenistic order, to be re-discovered and re-learned at a sooner stage than in OTL.
(Your own timeline, of course, provides a very beautiful scenario for a stronger Hellenistic world,
@Sersor. Also, in your TL, the merging of Hellenism in Massalia with the more practically-minded Gauls makes for a good excuse to develop a Hellenistic culture that truly values practical applications, far more than was the case in OTL. But the point remains that "more centres of knowledge" isn't enough all by itself. You need a more fundamental change, which results in "more centres of knowledge"
among other things. only then can the Hellenistic era be made to last longer-- which allows for the boost in tech you are after.)