Over the years, I have transcribed several simple Hindustani compositions in the Western style for the benefit of my non-Indian readers. My transcription is very basic and does not reflect all the ornaments for various reasons.
I'll quote here from my page on notating Indian classical music (where you will find a more detailed explanation of a few different styles of notating Hindustani classical music, including the traditional kind you've linked to):
Indian classical music is essentially an oral tradition. The emphasis has always been on training your ear. Notations tend to be very basic, simply providing the skeleton of the melody without the ornaments.
There are a few reasons why notations are not more detailed. For one, ornaments are more like variations on the main theme, and artists are free to personalize them to some extent. For another, ornamentation in Indian classical music is so profuse that it is not just labor intensive to notate all of it, it is also confusing for students.
Compositions play the role of helping students understand the flow-patterns of a raga's melody. Notating all the ornaments can be counterproductive, because it provides too much detail before the student has had a chance to get an overview of the melody structures - somewhat like trying to understand the pattern of fine wrinkles on a face before you know where the eyes, nose, and mouth go.
In other words, it is recommended that students learn the basic structure of a composition before attempting to replicate ornamentation, which is often acquired naturally in the course of becoming familiar with the music.
Having said that, my page on ornamentation in Indian classical music also uses Western notation symbols to explain ornaments. Here again, the intention was simply to explain Indian music to non-Indian audiences, rather than to adapt Western notation to Indian music. Again, I am not an expert at Western notation, so someone who is could probably do a better job choosing more appropriate symbols for notating the various ornaments.
You can find all of my scores on my Musescore page, but here is an example.