I saved a build using the skill chronicle and upon reapplying the build, the level was reset. This makes gaining skill points easy again and breaks progression for that build.

I am aware of this issue and have reported it to Puffish Skills, as this is achieved via their API. I am not sure that they intend to change how this works however.

It looks like additional API functions may have been added actually. I will look into this next update.
For context: pufmat/skillsmod#54

Awesome! Is there any way to manually set my level in the meantime, or would that require the new functions?

I think you would need to set your points back to 0 and then add experience until you reach the level you were supposed to be at. This can be done via commands: https://puffish.net/skillsmod/docs/players/commands