No, your conclusion is correct. Instead of using Time Machine for the SSD, try using a cloning program. That will allow you to reset Time Machine to backup everything.
Clone - Carbon Copy Cloner (Often recommended as it has more features than some others)
Thank you. I used to keep Carbon Copy backups before Time Machine came along (and before I switched to Mac in 2003)
I have successfully used Time Machine to restore systems or migrate to new Macs. The main purpose for the SSD drive backup is if I am travelling and my Macbook Pro fails. I can quickly replace it and restore the system and business data. The SSD card is lighter and faster than a hard disk for this purpose.
For now I will manually change the TM options to exclude folders when using the SSD drive for backup.
I have put in a feedback feature request to Apple.