These aren't "slight" modifications
Perhaps a workaround could be...
1) Randomize the answers of the first question (with the LS setting)
2) Use JavaScript to move the "fixed" answers to the appropriate places
3) Use JavaScript to create an array of the reordered answer codes and load it into a hidden question
4) In subsequent questions, recover the array (with Expression Manager or INSERTANS) and use JavaScript to reorder those answers according to the array order
It would require a fair amount of coding and the code would depend on question type, number and placement of "fixed" answers, etc.