Thx all for great advice. I bought a new cable from LBS and it was not the double-ended kind where you have to cut off the wrong kind of stopper-end, it just had the little barrel kind I needed, AND the tip was already very nicely soldered. It slid through the front gripshift and both housings like a dream! When I got a free bike off CL with a messed up housing, I should have never considered trying to reuse the cable in the first place!