Playing the non-melody strings

I love Shakespearian and other Early music, so I suspect this is a question for more than just my playing Greensleeves. In playing Bill Schilling's arrangement in Dulci-More there is a lot of playing on the middle strings. I've also run into using the bass string for a piece set to Yankee Doodle. For the bass string I just played that string by itself. On Greensleeves I'm uncertain if it's better to strum from the middle to the bass strings or just play the string alone.

Since there are several verses, I could start out just picking out the melody, including those middle strings; then play a verse with strums for all but those notes; then a verse strumming everything including strumming the middle and bass strings. (I strum out from the melody side.) There's a bit of open middle string playing, if that makes a difference. Is there something more I should know about pieces using more than just the melody/drone? For those without the book, this uses Aeolian tuning.