Create an overshot "inlay" ?

I am new to weaving and have a project in mind that will be overshot.  It is a violin blanket (basically it covers the violin in the case to protect it when the case is closed).  I am using precious hand spun yarn as the pattern yarn.  The top of the blanket I am weaving will need to be sewed to a backing.  I do NOT want to waste the precious hand spun yarn where it will be caught in a seam.

So my idea was to thread the outermost several edges on other heddles so they are only tied up and used for the plain weaving.  This is fine and I understand this part.

My question is, in the "inlay" section, do I need a floating selvedge or an extra end to weave around?  How exactly would this work?