For my second attempt, I decided to cut each strip/level of the primary hull from it's neighbors and join them butt-to-butt with several small pieces of scrap cardstock to reinforce them. You can see the strips backlit in this photo:
Cutting each "level" free allowed a cleaner join to it's neighbors and eliminated the warping and missed-cuts issues. While each piece was still damp with glue, I rubbed the inside of the part using a small bamboo skewer to help shape the joint. This method was more time-consuming (and more frustrating given my fat fingers and the size of the scrap strips) but it produced a much better result:
