I've had a go at altering the my surveys view so that it is read only and doesn't allow users to edit their responses.
Add a new menu item, type = BF Survey -> "My Requests"
Then assuming your category id is 1, copy the following files
/components/com_bfsurvey/views/1result/tmpl/form.php copy to /components/com_bfsurvey/views/1result/tmpl/read.php
/components/com_bfsurvey/views/1result/tmpl/form.form.xml copy to /components/com_bfsurvey/views/1result/tmpl/form.read.xml
Now edit the new read.php file. At the bottom change the submit button to a link back to the my surveys view, for example
<input type="submit" id="task_button" name="task_button" class="btn btn-large" value="<?php echo JText::_( 'COM_BFSURVEY_CATEGORIES_FIELD_SUBMIT_BUTTON_TEXT_DEFAULT' ); ?>" />
echo "<br><a href='".JRoute::_('index.php?option=com_bfsurvey&view=myrequests&Itemid=167')."'>".JText::_( 'back to my surveys')."</a><br>";
Now edit the file /components/com_bfsurvey/views/myrequests/tmpl/default.php
Change the layout in the link from form to read
$link = JRoute::_( 'index.php?option=com_bfsurvey&view='.$row->catid.'result&layout=form&id='.(int)$row->id );
$link = JRoute::_( 'index.php?option=com_bfsurvey&view='.$row->catid.'result&layout=read&id='.(int)$row->id );
Now as long as the user is logged in at the time of taking the survey, they should now see all their responses in the my requests view, and they will not be able to change the responses.
Let me know how you go.