OK, thanks guys.  Ed, that's exactly what I'm finding.  The leg tendons stripped out kind of fluffy and downy, and they soak up the glue really fast, maybe 10-20 seconds and they're good to go.  The back tendons came off in little wires, and they need some soaking, maybe a minute or so, before they'll do what I want.
I did size the bow several times.  Seven, I think?  It never did become glossy, but it does feel different from the bare wood.  Going to start laying some sinew tomorrow.  Wish me luck!  This is going to be a really cool bow.  Unless it explodes.  Then hopefully it'll be a really cool explosion.