Yes, I think so Steve.  A tight wrap of thread is extremely stong.  Others will have done that more than I have and I would defer to them, but I usually walk into my wife's sewing room and ask her to pick a nice color for me.  I'm pretty sure I use a poly-cotten blend and I super glue it down.  Certainly there are more primitive options, sinew and linen (flax) thread being the obvious ones.  I like the color options in modern thread.
Course just means layer when you're talking about sinew.  Normally, when I sinew back a bow I put 2 layers of sinew down being very careful to overlap the bundle ends.  However, in this case where you're holding down a sliver, if you make sure the problem spot is in the center of a bundle, you could get by with just a single layer of sinew.  That means you will pound/process less sinew.  On the other hand, if you're also wanting to hold some reflex or flat out guarantee the back is bulletproof, do a normal 2 course sinew job and you'll never have to worry about that bow's back failing.
I wouldn't give up on putting different pieces of osage together either in a takedown or a spliced stave.  I do it all the time.  Normally I find that different weights in osage billets are caused by different moisture contents.  Are you sure both pieces were dry?
George