Looks like you have already discovered the problem. First time I ran into that I was a bit shocked as like you the CA always thickened up when it went bad. This stuff looked fine but wouldn't kick, almost drove me crazy till I tried a new bottle.
I have built a bunch with laser cut wood and CA, never had a problem, in fact I read someplace to not sand off the burnt areas. Guess you just have to do what you feel is right for you.