We ended up watching the leatherback turtles on the Gandoca beach. This was organized through an agency in Puero Viejo de Talamanca (I can’t remember the name of the agency). I can certainly recommend this option, and after reading more about turtle watching I think it is actually get by far the highest probability of success in April.
There are at least 2 tours that I could find that could fit your criteria:
and
LeatherBack Volunteer Vacation
I am sure that you could probably get to those beaches on your own if you choose to but I think these would be better. There is actually a whole slew of tours just like those at SeeTurtles.org
EDIT
More on Turtle Watching in Costa Rica
Credit:stackoverflow.com‘
4 Mar, 2024
4 Mar, 2024
4 Mar, 2024
5 Mar, 2024