Change the input format for 3000+ nodes
I'm going to preface this answer by saying doing this en-masse presents a potential security risk, especially if you are changing the format to a more lenient set of filters. Text formats modify field output during display, not during save. So for example, any previously-escaped HTML or PHP submitted to a field will straight up render/run if you accidentally or intentionally set the filter to Full HTML or PHP code. 

It's for this reason that Drupal doesn't automatically update all existing nodes when you change a text format. The behavior of text formats in similar scenarios is still an open issue.

So again: beware, there be dragons.

With that said, each field stores the text as a column named field_foo_format, where field_foo is the machine name of the field. You'll need to update that column on the tables field_revision_field_foo and field_data_field_foo.

The value for the column is a machine name defined as the column format in the filter_format table. So, updating all the fields would be a matter of a query like:

UPDATE field_revision_foo SET field_foo_format = 'new_format';
UPDATE field_data_foo SET field_foo_format = 'new_format';


for each field that needs changing.

You can determine new_format value here: http://YOURSITE.com/admin/config/content/formats - configure link - number or string in URL is your new_format. Clear cache after updating.