Yeah, I guess "sentimental" is too schmaltzy but doesn't "for old times' sake" means "to remember the good times spent together" ? Because something that has a sentimental value, in the french sense of expression, is something that has a an intrisic value, such as the gift your grandmother gave you, or any object that you care about not for its value in money but for its "memories" and "meaning" value.
Yes - in English it means exactly that too - "why do you keep that ugly old painting? For sentimental reasons, my Grandmother gave it to me". However, I can't imagine one guy ever saying he wants to work with another for sentimental reasons - unless it's strictly in that schmaltzy context where perhaps we are talking about a butler who has been with the family for years.
-That guy's terrible! He spilt all the wine. Why do you keep him?
-Oh for sentimental reasons, he's been with the family since I was born!
From what I understand from your original post if you want to work with someone because of a shared past - even if, clinically speaking, he might not be the best person for the job - then that's for old times' sake as if you owe him a small debt from that shared past, not simply to reminisce together.