The proposal is pretty simple: we propose an extended Tamil alphabet. The proposal maps Devanagari alphasyllabary (that is, the Hindi/Sanskrit alphabet/alphasyllabary/abugida) one-to-one to the extended Tamil alphasyllabary. It works as follows.
(1) consider the Hindi alphasyllabary. It has two sections: one for the vowels and one for the consonants.
(2) Let the vowels in Hindi map one-to-one to the existing vowels in Tamil. This mapping remains the same.
(3) The consonants in Hindi are in two subsections: the first subsection is the famous 5x5 consonant layout of Sanskrit. The second subsection is the remaining consonants: ya, ra, la, va, et cetera.
(4) Let the consonants in the second subsection map one-to-one to the corresponding consonants in Tamil.
(5) The leaves the last subsection: the 5x5 grid. This is mapped quite simply as follows:
(a) use | | to soften a sound.
(b) use ( ) to retain the existing sound. (Or use nothing.) Note that adding parentheses around an expression in mathematics does not change its value.
(c) use the consonant "ha" to add the aspirated sound.
(6) In addition to this, use the "(" symbol to mimic the "chandra" symbol in Hindi going on top of a character. The "(" after an unmodified Tamil consonant/"a" Tamil letter modifies the sound to "a" as in "cat", and the "(" after a long Tamil consonant/"aa" Tamil letter modifies the sound to "au" as in "caught".
All this is quite clear from the schema below.
Did not include one thing in the graphic: using the "(" symbol. It is used as below.
pal = ப( ல்
pot = பா(ட்
Al = அ( ல்
aught = ஆ( ட்
Very simple and very clean.
Update (April 9, 2016): there is one typo in the above graphic. It is the "na" with the three swirls in the third line, not the "na" with the two swirls.