School is as important as you make it. Let this be a learning opportunity. Choose your options based on instructors. Do your homework on their backgrounds and teaching style. Think about what you might be able to glean from their instruction, regardless of what the project is. Then go make the most of it. Worst case scenario you have one fewer page in your portfolio, which might be a plus in the long run. Best case scenario you find you like what you've taken on, or you find a mentor in a new instructor.

There are lots of possibilities, many of which you won't be able to predict. Don't let your preconceived path get in the way.

Figure out which of the shitty options will require the least amount of your time and do that one.  Use the extra time to use the school environment/resources for something meaningful to you and your career.  Maybe add an independent study or elective class that speaks to you interests.   A quality part-time job with an architect might be a good option as well.

Choose the project you’d either enjoy least or find most difficult. 

you get out of it what you put into it...

Take the one you find the least interesting and make it happen.  You'll likely learn something.

keep in mind that finding interesting possibilities in ordinary projects for mediocre clients is the essence of what even very successful architects do. this is a good chance to practice it ;)

The lesser of two evils is to go with a professor that is organized, professional, and delivers on their curriculum promises even if you don't see eye to eye design wise. Having a solid studio professor will positively impact your peripheral classes. Try to think long term, hopefully one of the studios will be a new type of project in your portfolio not currently in your selected work. Even if you don't see it now, there is no telling come job application season.

I honestly don't think you need a professor to like "personally" ... I think that is highly subjective and mercurial. Too many professors just fixate on younger versions of themselves. One of my most successful studios in graduate school I was the professor's least favorite student.  

Some terms are duds. It happens. I would pick the most organized prof and the most structured studio. No surprises, straightforward term, do other things with my time.

Can you do a design competition as an independent study/studio with an instructor you like? I did this for the Urban Land Institute, bonus you have a chance to win some cash as well.

You will only know if it is or is not possible if you ask if you don't ask you will never know if it was possible. just don't tell them the studios are not good as a reason for an independent study.

Over and OUT

Peter N