I like malayalam. It has a calming effect hearing something go by so quick. I guess I can understand better than most Tamilians being from the border area + family ancestry etc. Definitely understand it lot better than Kannada and Telugu....and even what passes off as Tamil in Chennai a lot of the time. They retain lot of sanskrit words too, makes it easier in my case these days. I found later in life the numbers I use are essentially malayali rather than pure kaveri + eastern tamil too (nallu, anchu versus nanku/eindu for four/five etc)....definitely its somewhat of a language continuum in many regards.
Lot of great poetry came from the Chera age, back when still west coast Tamil "dialect" there...but many will tell you Malayalam has much longer history....in fact when it diverged from "Tamil" in a standardised definable form, I would date back to much earlier than 300 years. Maybe 700 at least. But very mututally intelligible during that period even, for longest time as a kid I thought the Jnanappana and other nice poems were Tamil. ...because even in Tamil there is much variance in register/dialect etc depending on the particular area of origin.
Of course you would have gone through these experiences. What you have just explained is something that I stopped trying to convey to those who advocate, for present-day political and societal reasons, the absolute cultural autonomy of the Indus Valley region. This is my less-than-worshipful phrasing; an advocate would have put it differently. But you have described the language continuum that exists all over, not just between Malayalam and 'eastern' Tamil, but elsewhere, all over India. We already have talked about the equivalence of sibilant and aspirate between cis-Indus and trans-Indus dialects of Indo-Iranian; in a far removed location, where the attenuated wash of Indo-Aryan aka Sanskrit and its accompanying Prakrit met the eastern languages that have nothing to do with either Indo-Aryan or with Dravidian, we find the same or similar. From Odisha or whatever they are calling their region these days, running across north-east to the Brahmaputra Valley, there is an identical shift, from the strong dental 's' ranging through the increasingly accented versions of mid-Bengal, until the Valley recognises the 's' sound but writes it with a 'ch'. That leads to some decidedly infelicitous results; north Indians find one combination, the kingdom of the Sutiyas, irresistible; in Assamese, it is spelt 'chutiya'.
Back to your note. I remember, as a 'furriner', how difficult I found adjusting to quarrelsome, squabbling Madras (as it still was when I shifted), and what a relief it was to listen to the Tamil of Madurai, and to deal with a completely transformed, far more dignified and respectful culture, where you counted for something as long as your manners were in place. It isn't just the variance in register or dialect, there are huge cultural distances, even in as homogenous a state as Tamil Nadu. Some attribute it maliciously to the influence of the immediate northern neighbours.