The problem with using technology to simulate 'best practice' is that best practice doesn't seem to survive in ASoIaF. Instead, it seems to be established by 'great men', who use it to further their own ends and careers and consequently keep it a closely-guarded secret.
In Weberian terms, you could say that administration is charismatic rather than rational-mechanical. Take Littlefinger's accounting techniques, for instance - no one can wrap their heads around how he makes money appear, no one seems to be particularly interested, and he's certainly not going to tell anyone (partly because it turns out he was just taking out loans). When Littlefinger is gone, his replacement has no idea how to manage the Kingdoms' finances; there isn't generalised knowledge of that sort, except in the form of the Maesters, who are effectively a secretive guild of general experts and have an interest in limiting the accessibility of knowledge to themselves.
Varys is another case in point. What he does isn't based on a generalised theory of espionage, but rather on his own personal competence and charisma. To replace him, they need to find someone with his own way of doing things. The only kind of training in administrative functions seems to be practical experience, outside of the Citadel.
So if we implemented technology, it would have to be assumed that, when the economic technology level increases, it's because Littlefinger, say, develops and records, systematically, his techniques, such that anyone studying his records could learn them, and that there are people who are trained in them. Note that educational institutions other than the Citadel don't seem to exist in Westeros. That doesn't happen; Littlefinger's knowledge will die with him. For that situation to be modelled, the technology level would have to drop every time a councillor is replaced. The same applies to military practices; a brilliant general in Westeros doesn't institutionalise their methods such that they persist after the general's death.
Indeed, technology seems to have been in decay for a long time, if anything, as it sounds like at the time of Aegon's conquest, magic - arguably a form of technology - was used for things that people at the time of the books' setting don't even remember. Even (presumably) non-magical technologies such as wildfire seem to be lost quite easily - the lack of any educational infrastructure for the preservation and distribution of accumulated knowledge means that, even when new discoveries are made and used, political disruption can cause them to stop being used. The use of wildfire was never generalised, for example, because the Targaryen kings had an interest in keeping it secret, and if it were to be generalised, it would be to the disadvantage of the ruling class - it would entail greater investments in warfare and potentially destabilise the social order, as it would enable knowledgeable but relatively powerless agents to use incredible force (a petty lord - or worse, a revolting peasant leader - could theoretically blow up the Red Keep).
The stasis of society is probably the most significant contributor: if someone did invent the steam engine in Westeros, why would it lead to an industrial revolution? Hero of Alexandria described the steam turbine in the first century AD; no one realised its implications because the agricultural economy, as it stood, functioned without the need for powered locomotives, and their introduction would have seriously destabilised an economy based on the exploitation of slave labour, and in turn the whole socio-political situation in which the acquisition of slaves through warfare, provision of land for the soldiers needed to acquire slaves, and so on, was fundamental. In Westeros, who would have access to that knowledge and not, at the same time, a vested interest in maintaining an economy based on the exploitation of the peasantry? Even if such a person did exist (Tyrion might be sympathetic to their plight), how could they convince enough people to take up the new technology? It would be against the interests of the entire power structure, and there's no nascent class (such as the bourgeoisie in our industrial revolution) to use it to the end of seizing power.
If there's some other variable that increases incrementally over time in the world of ASoIaF, technology could perhaps be used to simulate that. I can't think of one off the top of my head, though.
