Filter Content Cronologically Based on Current Month
I can't think of a 'clean' way of doing it within the Drupal interface, but it should be doable by using a template. An override of views-view-table.tpl.php (or the list version of that) and then test the dates as they come through.
It would be a little tricky to know which block has been previously put up (and therefore where to start the next block) but I think it is possible.

In more detail. 


Create a view with the listing that you want (for all months).
Create three blocks within that view (they can be the same).
Using the Theme Information tab, find the name of the template that
handles the rendering of the rows.
Put code in that template to only take a months worth of dates at a
time.
Set a flag that 'Feb' is done, so next iteration will be 'Apr'.