Creating teams based on student preferences

Problem Description

Each year my 8th graders participate in a group project. Groups of 6 are ideal, however due to math, some groups have to have only 5 in them. I give them a Google Form teammate preference survey. Each column has the entire class's names in it. Column A is where they select their own name. Column B is their first choice of teammate, Column C is their second choice, and so on down the line. What I need is a way to take the results of this survey and input them into something that will maximize all students' preferences and do its best to guarantee that they are with as many people on their survey as possible to increase student buy-in to the group project. I need something reusable each year for each of my classes. I have tried several different websites and apps out there (including Shuffle Buddy) but none have met all the criteria above.