The talam of the song looks pretty much straightforward - adi talam or 4/4 in western. This is true for most of the song. When we come to the interlude under discussion, the tabla still plays the 4/4 rhythm. However the chorus melody is composed in 7/8 (misra chaapu). Misra chaapu is generally 3+4 counts. For example, tha ki ta ; tha ka thi mi. However this one seems to be 4+3 counts, which is: tha ka thi mi ; tha ki ta. I read somewhere that this talam is called "vilOma". Please correct me if I am wrong. That was very nicely done - mixing a 4/4 rhythm with a melody set in 7/8.
So I went ahead and tried to add 7/8 beats to the song, and here is the result. Somewhere in the middle, the melody changes to 4/4, but I couldn't find out where. This combination of talas necessiated the extra theermaanam at the end of the interlude. Use headphones to hear the below piece. You will hear the original song on the right speakers and the 7/8 rhythm that I added on the left.
You can also follow this interlude, by putting the misra chappu talam in half the speed of the rhythm that I had played. That means, 1 "gubu subu" is 1 count.
There are a few instances of other such experiments too. I think the most talked about of them is "aagaya vennilave" from "arangetra velai". People say that the song is in roopakam while the tabla plays in 4/4 adi talam. Some time back my opinion was that the song as a whole was in 12/8, and hence the 4/4 rhythm will also suit this song. I am not sure on this though.
I also heard a mridangam player talking on radio. He was saying how tough it was playing for a song by ilaiyaraaja, where he had to play 4/4 adi talam, while the composition was in 7/8. I don't remember the song. You can imagine how tough it would be to play a completely different tala in a live orchestra. These days, with the help of technology, it is pretty much easy carrying on such experiments.
The song "Chinnan chiru vayadhil" from "Meendum Kokila" is in 3/4 (roopakam). After the 1st stanza, during the pallavi, an extra metal sound is heard in 4 counts overlapping with the 3/4 rhythm. This 4 counts may be perceived as a 4/4 or rather 6/8 meter.
One more often used thing is playing an occasional 6/8 theermanam / drum roll on top of 4/4. This is pretty much easy and hence I am not discussing that here. Do you know of any other similar complex experiments?
Finally, I don't know much about talas. So kindly correct me if there are any mistakes in this post. You can point them in the comments section.