Where to go (& not to go!) during Songkran 2016

Honestly, from what I remember, Song Kran is not as bad as some of the other national holidays. Maybe more people spend this particular holiday with family and playing with water, and not so much traveling. At least, from what I remember in Khao Yai it is not as extreme as some of the other public holidays. I expect Song Kran could be big around the Phetchaburi river in Kaeng Krachan town, but not sure if the park gets much more busy than on normal weekends. Maybe others on this forum have spend Song kran there...?
Though it will probably not be quiet in any of the parks.

Yes, there will be a mass exodus.
It's a bit hard to predict. Normally I think the 11th is one of the worst days to travel. But this year the 11th is a monday, and perhaps people travel in the weekend on 09 or 10? Still expect long traffic jams on the few days prior the official dates.
And around 16 - 17 it will be just as bad only opposite direction, back to Bangkok.

I would guess the road North, so to Huai Kha Khaeng, might be the most quiet during these days.
In previous years I know it has taken people about 7 hours to get to Khao Yai. Normally it should be 2.5-3 hrs.

Of all the parks in your list, I guess Pangsida, Huai Kha Khaeng and Phu Khieo will be the most quiet, just as usual.
It was busy last night in Pangsida. Busy for Pangsida standards, probably 5 or 6 cars at the camp ground, haha.