Yes, you're right, the grounding is for stability.
Excellent work! I should say, the Diodes, they are acting as Directional Devices, the Resistance on one path is different from the other path, thus the Duty Cycle can be adjusted ever so slightly, but the video is not the best way to do it, as you noted!
The stages help, start with a Frequency Stage, push this on to another stage and start looking to adjust the Duty Cycle on another Stage, this way the Duty can be adjusted without affecting the Frequency. Because they are on different stages:
I hope this makes sense.
One of my Breadboard Prototypes: Notice no Grounded Inputs in my layout...
I started the same as you!