Headcanon: one of the reasons why Gallifreyan is a) so complex, and b) so inconsistent, is because it's less one language and more a complex mishmash of thousands of languages and dialects.
Think about how one of the reasons English can be complex to learn is because of the mix of Germanic and romance language roots, and now take it up to 11.
While one might expect Gallifrey to be monolingual, given its age and class structure, this probably isn't technically the case. After all, why limit your culture to one language when the average citizen is effectively panlingual (to the point that TARDIS translation circuits are actually dependent on their pilots' knowledge, rather than the other way round)?
Thus, if there once were distinct languages on Gallifrey, they probably have all been merged at this point into modern Gallifrey's super-Esperanto. Add in loan words from notable civilisations across all of spacetime (but likely primarily from Gallifreyan colonies and allies like Dronid, Minyos, Cartego etc.), and it quickly becomes quite unwieldy.
It's also likely that there's a lot of overlap between these sub-languages, which can make distinguishing meaning hard to an outsider. Gallifreyans likely get around this courtesy of their telepathic connections.
TBH, given Time Lord sensibilities, it's likely that every single word variation has its own delicate meanings, derived not just from their societal uses but also from the etymology and history of each one. Canonically (though I don't have a source) we know that there are 30 different words meaning "culture shock", for example, which likely have very minor distinctions in meaning. We also know, unsurprisingly, that there's at least 208 tenses to help in describing time travel.
As an example - imagine being a Sunari ambassador at an embassy gathering and accidentally offending every Time Lord in the room because you accidentally used a definite article derived from the memeovored Old High Tersuran colony dialect, now considered low-brow by association with modern Tersuran, when you intended to use a nearly identical form of the word originating from the Founding Conflict, a triumphant post-Rassilonian intervention, distinguished by a near-imperceptible glottal stop.
It's likely that some of these Gallifreyan sub-languages/dialects may still be spoken with increased frequency under certain conditions, such as in one's own House or when visiting other city complexes. We know, for example, that Arcadia seems to be associated with a "Northern English" accent (which Nine picked up subconsciously post-regeneration, with the Fall of Arcadia being one of the last things the War Doctor remembered before DOTD's multi-Doctor event - hence "lots of planets have a north") when translated, which may indicate some dialect differences in the original language. I suspect there is a societal expectation for Gallifreyans to code-switch depending on the situation, with Citadel business generally expecting the Gallifreyan equivalent of RP, though it's relatively common for Time Lords less concerned with respectability and politicking to not comply.
One nice benefit of all this complexity, and the reason I made this post, is that there's a good argument to be made that every fan attempt to construct a Gallifreyan language can be 'canon', contradictions and all.
Greencook Gallifreyan? A formal evolution of Pythian prophecy scripture into the post-Intuitive Revelation era (based on its similarities with the Visionary's scrawling in The End of Time).
Sherman Gallifreyan? A modern katakana-like phonetic alphabet for the rapid-onslaught of new loan words following President Romana's open academy policies. Recently adopted by the Fifteenth Doctor for writing human proverbs.
Teegarden Gallifreyan? An archaic but recognisable near-Capitolian dialect from the Prydonian mountains, once spoken by Oldblood houses like Lungbarrow and Blyledge.
Or, in a nutshell, the state of Gallifreyan conlangs (and maybe in-universe Gallifreyan dialects):
I guess the dream project would be to accept the complexity and create some sort of grand modular "meta-Gallifreyan" conlang, merging as many fan interpretations as possible with their own distinctions and overlaps, that can continue to be updated as new ideas come up and new stories are released...