The note about CA and old wood was correct. Older wood will likely have a lower moisture content, which precludes CA adhesives from curing properly. Going to carpenter's glue solves the problem.

The accuracy of die-cut parts and laser-cut parts is moot. It all depends upon how accurately the original parts are drawn. I've seen laser parts that were not too accurate because the original drawings they were made from were not that accurate. If the kit manufacturer makes quality dies from quality drawings, die-cut parts are as accurate as any other way of making parts.