Thanks for your willingness to help, but I think I need to clarify myself. I'm probably falling prey to the XY problem here.
My primary goal is instead of my custom classes showing up as <S3: myfhc> (see column foo), I want to specify how they should be seen when 'printed' in this context. I don't think I'll have any trouble writing up that method; but finding what method I need to specify is the tricky part. It doesn't appear that behavior is determined by the format generic or the print generic. (In fact, when I print this table in the console, I get a much more reasonable output than <S3: myfhc>, it actually includes values.) I'm dumbfounded on how to find the function that RStudio uses in this case.
I was hoping that finding that method would lead me to source code that shows the right method I need to implement, but that may be difficult too.