Just a brief update, without pictures yet... I've built the rocket pretty much as described below. I haven't weighted the nose yet... I rechecked the figures and discovered that the rocket has 0.93 calibers of stability without noseweight with a C6-7 mounted; I think I'm going to launch it that way. RockSim calculated an altitude of just a hair more than 1200' with the 1/8 ounce I originally planned, 1211' without it, so it isn't exactly a show-stopper to add the weight. Still, I'm going to try without it.
As a consequence of a conversation on Ye Olde Rocket Forum (this one right here), I have decided to design a fat but hopefully high-flying rocket based on the Baby Bertha (with one part added). Since Baby Bertha-based designs are often called "goonies," and since this design resembles a rocket propelled grenade, I've named it the Rocket Propelled Goony.
I used the trial version of RockSim to create the image above, and to verify stability; as designed, with a C6-7 mounted, it's marginally stable until you add about an eighth of an ounce of nose weight. RockSim is cool, but frustrating in many ways... like, every time I load this file, the fins have moved back a quarter inch. So I drag them forward, save the file, and when I open it again they're hanging off again. Gah. But if you'd like to download the RockSim file for this model, go ahead and click here.
According to RockSim, this design should fly best on A8-3, B6-4, and C6-7 engines. I was pretty sure those were the optimal engines before I ran the simulations, but it is nice to have corroboration. According to the simulation, on a C6-7 this rocket should make it to about 1,200 feet... pretty decent for a pudgy design like this one.
Probably more useful to someone wanting to build one like this is my template PDF: RocketPropelledGoonyTemplate.pdf. You can print the transition (the first page) directly on 110# cardstock to make that part. The second page contains the fin template.