You're pretty much trying to make a Nessler Ball.
In the 1850s there were numerous attempts to make a self stabilizing bullet to make smoothbore muskets, then obsolete, more effective until those units received rifled weapons .
To this day it seems hard to get them to shoot well, the over riding theory being these were more psychological in effect to make the troops feel like they had "bullets" similar to a Minie vs "outdated" round balls.
Test show the Nessler only improved over the round ball at 200+ yards and was actually less accurate at short ranges. They had a short service life, the CSA used the type shown in the bottom pic as well as the top pic , but to my knowledge after 1865 no military used them for anything. I bought 60 of the Nesslers in the bottom pic to try in my Pedersoli 1816 Springfield but haven't shot any yet. They mic at .680, I'm guessing I'm going to have ok results just hot dip lubing them and running them through a .680 sizer, and shooting them like Minies.
The idea being that the base will "collapse and expand" into the bore on firing and the bullet will use gyroscopic properties to stay pointed forward.