I agree, water content. You mentioned in the first video its too wet at first. You're right. That was way too wet. But afterwards it looked drier when you were shaping it? Correct me if Im wrong here. Water content is actually super important for good concrete ammo.
What I usually do is get it really close to the correct water content, shape it roughly to the desired egg shape (by hand/meatballer) then lightly spritz it with the water bottle. The amount you can add to the water content with a water bottle is very even and controlled.
I "think" you're having issues because of the plastic eggs. Dry enough not to stick means not enough water. Its possible you can spray it with the water bottle but it seems like thats not adding an even enough water content throughout to make the optimum cure. That's my best guess. Any "gluing" is really sensitive to correct pressure vs "wetness". Also might not hurt to always wash the sand. Correctly done the strength is much, much higher than when things are just slightly off. Doesn't seem to be much room for error.
As for compressing you will feel the mix shift within itself as you compress it. A little too wet and its like compressing mud. i.e. impossible. A little too dry and you wont feel anything shifting either. It's all about the ratio of water. Might also have to do with the type of aggregate I was using personally, but I would be surprised if you couldnt compress those at least a little.
If everything is correctly made and compressed you can take the just made ammo and lightly knock it on the table (work surface) and it wont affect the ammo shape or break. It will almost feel set, Although if you tap it too hard you will see otherwise.
The best/strongest ammo I've made was with a meatballer. You can really put a lot of pressure on the ammo when making it. The steps are spray meatballer, dip in fine sand, shake off excess, put your mix it, squeeze like hell and take out.
I had one set that was particularly strong where for kicks I threw by hand point blank at the concrete road and it didnt break after three or four throws. These were hard throws too. Anyways, it will outdo clay by a long shot.
EDIT: I have never checked density but I would estimate it is within 10-20% of a good river stone. That's my wild guess, don't quote me on it.