After the above was written, on its 14th flight, the upper stage motor (an A3-4T in a 13mm adapter, CHAD staged) failed to ignite, and the rocket lawn-darted from about 50 feet. The tube was badly crumpled a few inches forward of the fins, beyond repair. I plan to cut the tube foward of the fin unit and ream out the thrust block, and thus convert the sustainer into a booster to replace the middle stage lost the first time my Mongoose 3 flew.
The experiment with conversion of the rocket to a booster was a failure -- the forward centering collar, which holds the motor mount in place in the fin unit, was too long for a booster, and I also found that two of the fins were cracking at their bases from too many hard landings. The remains of the rocket were consigned to the trash, with only the nose cone and streamer kept for other use. The nose cone has since been passed along to a child whose Alpha III separated, losing the cone; while it's a different color and a longer ogive, it'll fit the Alpha III body and let the child fly again with minimal cost to repair. I hope to see the rocket so repaired at the November launch in Monroe, with (presumably) happy child in tow.