A good 'trajectory' might be hard to plot, since extraversion and introversion are very complex, highly hereditary (as recognised by Marti Olsen Laney, PsyD) and so forth. Still, we can try.
If we're trying to reduce the extravert:introvert ratio, I'd say we have two main tasks: (i) make the tangible and intangible environment more likely to give rise to introverts than it was before; (ii) empower introverts to have greater reproductive, and similar forms of, influence.
(i) No doubt you've heard some variant of the saying that architecture/[insert thing] is a reflection of society and vice versa. Well, as cliche as that sounds, it often makes a certain sort of sense. Basically, you'll need to change the general infrastructure, material or otherwise, so that it promotes introverted behaviour more than extraverted behaviour.
(ii) The first thing we ought to remember is that we don't need to make sure every introvert is thus empowered. Because of the mild flexibility of your requirements, we can say helping a large fraction of introverts and 'potential' introverts to help themselves will do the job.
Steps you can take
- Mostly addressing the behavioural manifestation of extraversion and introversion: Tweak the tech path to make urban planning more suited for lifestyles that we would call introverted. Nice 'traditional' architecture, resource-frugal cities...
- Addressing an underlying mechanism of extraversion and introversion: Give humankind reasons to limit reward sensitivity. This does sound exceedingly vague, but to give a concrete if not precise example, instead of letting the physical and socioeconomic environments be highly motivating, stimulating, exciting and energising to extraverts, have them be full of suitably sized traps that people are certain to fall into if they just seek rewards blindly. Also make it such that if these traps are bypassed there are many, and substantial, returns on investment, so to speak, to encourage 'introverted thinking'.
- To take a slightly different perspective, allow low-impact crises that must be solved by reflection rather than blind socialisation to happen irregularly and very frequently throughout world history, encouraging the introversion-associated tendency to plan.
- Addressing an underlying mechanism of extraversion and introversion: Indirectly discourage ready or high mental arousal by reducing certain basic reasons for arousal. Come up with creative reasons for island-like or similar communities to be the norm. If you want idea competition to keep going strong even in this environment; that is, if you don't want a bunch of insular societies; no problem, since it isn't mutually exclusive with 'island-like communities'. But you'll have to get creative again.
- Changing societies to favour introversion: Cultural shift is extremely difficult to predict. You're very lucky you're an author of alternative-history fiction. To 'turn the tables' on extraversion-biased cultures in such a way that the introvert advantage will last five whole centuries, even approximately, there are few shortcuts. You could try the following.
- Training. (This is not to be confused with education. You do not grant individuals competence by blogging alone.) People with sufficient time and money might produce analogue and, should the world be 'sufficiently far along' technologically, digital tools introverts could use to be better at achieving their social-interaction-related goals out there in the jungle of society.
- Appropriate involvement in politics. Specifically, introverts in extraversion-biased cultures must make tremendous efforts to reduce the incentives that favour those who seek power. But they must be subtle, because presumably extraverts seeking power will have people and other resources on their side and rally these resources against behaviour they find objectionable.
- Cutting losses. Introverts may wish to, if possible, associate less with people who use others as an emotional crutch rather than functioning by themselves. Also, introverts could better pick their battles and go off alone to express their intellect, imagination and planning for the future instead of arguing with people who see no value in doing so. (I'm not recommending that introverts treat poorly the friends, family and neighbours they have reason to treat well!) All this must be gradual, since opponents probably have many weapons they'll let loose at the slightest hint of provocation. Note the possible unexpected difficulty of doing this as a member of a complex technological civilisation where almost every person depends on lots of other people.
- Notable suggestions that may or may not further your goal:
- You probably can't stop the rise of highly scalable communications technology and usage of such technology for entertainment, but you can have introverts, as individuals or in small groups, mount defences against the overreach of such technology and entertainment.
- Extremely delayed invention of philosophies that would urge that involuntary institutions provide support for the well-being of people and society. This would lead to a change in the nature of social interactions. Whether the likelihood ratio of extraverted behaviour to introverted behaviour would really fall remains to be seen.
- Increased aversion to economic decisions that reveal 'sociability', impulsivity and status-seeking tendencies. Since things such as modern advertising techniques rose to dominance in the 20th century in real-life history, this aversion probably has to be introduced earlier to have less risk of being instantly negated. Food for thought: was economic choice always possible for individuals and large groups, and has this differed between societies?
- Everyone has both introversion and extraversion as elements of his/her personality. And not only does a personality have the capacity to make you do either 'introverted' or 'extraverted' activities, but people also display different personalities in different contexts. Come up with a concerted decades-long public-relations campaign that appeals to overall-extroverts' introverted side(s) without making it explicit (else they might start their own, opposed PR campaign just for the sake of it). Obviously, patience, money and dedication are required even to prevent such efforts from fizzling out or turning counterproductive.
I did my best, and found a few roads to the goal, some of which would indirectly lead to increased genetic (genetic $\approx$ sustainable) dispositions towards introversion, but that's all. If you think about it, 500 years is very long.