Cochin-Munnar-Thekkady-Periyar-Allepy can we fit Kovalam? What to cut out?

I am spending 15 days in India with my partner and am trying to refine our time in Kerala. We definitely want to spend time on the backwaters in a houseboat for at least 1 night, maybe 2? A family friend in India has proposed the following itinerary:

Arrive 28 Jan
Mumbai (3 days)
fly to Cochin
Cochin (PVT Tourist Car fr 2)
Munnar (2 days)
Thekkady & Periyar (2 days)
Alleppey (2 days)
Train to Chennai
Chennai (2 days)
Depart 12 Feb back to USA

We are not as interested in seeing the wildlife reserve but instead would like to mainly rent a bike and bike around Munnar, see a tea/spice plantaion, and as I mentioned above, do a backwater boat tour overnight. Is 2 days too much time to spend in Munnar/Thekkady & Periyar? I assume the 2 days in Alleppey is for the boat tour. Originally we thought just 1 day or 1.5 days in Munnar and then the backwater boat would be enough to accomplish this, instead of the 6 days and 4 locations above.

Also, we were hoping to work in some time in Kovalam, which is quite a ways south. Is there a way to fit this in to the itinerary and still take a train (overnight?) to get to Chennai? Another option is to add Pondicherry, but as that is not in Kerala, I will save it for another thread.

Thanks in advance, we cannot wait to visit!