I have built quite a few Core-house foam wings and many Jeff Dawson combat wings
In each case I try to use a sandpaper wrapped square stock the width of the routed out spar groove to clean up that area. I lay carbon TOW in the spar groove with watered down wood glue and then add in the spar. Once it is all set up I place tape on either side of the spar and use a small plane to shave the excess sticking up down to the tape. At the tips where there is a lot to remove I work from the center out to the tip.
Fred, the tow should be epoxied to the spar. White glue is very soft. Maybe make a jig to hold the spar with a bend in the middle. You really only need a foot or less across the centersection. The best bet is to use vertical spars with ~6in. of tow on the BACK of the spar before gluing it in and planing it down. The spars generally fail by cracking in tension on the backside when the plane hits nose first.
The best way to use tow is Steve Hills method on the Arrowplane. wrap ~10 inches around the boom at the trailing edge. Twist it tight against the boom and then use a small drop of CyA, preferably the gold Foam Safe stuff. Then run it out to the tip and secure with CyA. Apply epoxy or white glue along the trailing edge to saturate the tow. This keeps the wings from folding forward as far in a straight in crash. Judging by how the wing wrinkles develop in a crash the wing tips apparently swing forward 2-3 inches, or until one tip hits the ground.
A patch of carbon fiber matt about 3in x 12in epoxied across the center at the trailing edge helps a lot too.