Passing parameters to WordPress static front page

I have a custom plugin that shows a series of custom posts on a page, i.e.

http://www.example.com/permalink/

On that page I have a form to filter the posts according to a number of different parameters, and it is passed as:

http://www.example.com/permalink/?param1=1&param2=2&param3=3&param4=4&pagi_page=1

The problem: If I change that page to be the static front page, the custom posts are still shown, but if I try to apply a filter it loads the posts archive.

I know it has something to do with the permalinks and .htaccess, but I have no idea how to solve it. If I turn the permalinks to ‘plain’ and manually enter the page id it works fine (like this):

http://www.example.com/?page_id=6&param1=1&param2=2&param3=3&param4=4&pagi_page=1

But if I change the permalinks back to the Post Name it doesn’t work.

Any help very much appreciated.