Water is complex; surface tension like effects can happen in thin films of it other than at the surface. At greater speeds, these are reduced so the Magnus effect is reduced.

So what allows for directional sweeping to make the rock curl even more than it normally would on its own?

And why does the same directional sweeping technique, except applied in reverse, cause the rock to curl less than it normally would on its own?

And why does applying sweeping with both techniques at the same time counteract the directional movement?

Roughening the surface by sweeping thins the film at many points. Your latter two points are more interesting; flow is unlikely, but directional "surface tension" effects (actually organized Van der Waals forces) are certainly possible, given that water is an asymmetrical molecule (which is why surface tension happens at all.)

As a follow up, what causes negative curl (when the rock curls in the opposite direction of rotation)?

Not something you are bound to see in professional level arenas, but not uncommon in clubs.

In fact, what makes club ice seemingly impossible to make behave like arena ice? There is a serious amount of research by Canadian universities that has gone into trying to make club ice act like arena ice for training purposes and the best we have been able to do is "almost the same".

Shitty ice.

To add: Curling on ice used for other purposes too leads to shitty ice. The ice needs to be flat and level. Zambonis do not lead to level ice. Dual purpose rinks likely also don't shave the ice to ensure level and flatness. Likewise, gouges in the ice from skates causes unpredictability and some might compensate by over pebbling prior to playing. Also poorly/sparsely pebbled I've can lead to unpredictableness.

That goes without saying, but what are the exact mechanics?

To your edit:

> Curling on ice used for other purposes too leads to shitty ice

Certainly skating ice is a whole other beast to curl on, but I'm talking about club ice: Ice that is only used for curling.

The club I curl at is strictly dedicated curling ice and most curlers there take care and pride in the ice and work to keep it clean and in to condition. But we are also open to introducing people and bringing new curlers in. Sometimes people don't wear ideal clothing. They will wear clothes that is linty/fuzzy. Some lint or fuzz gets in the ice and a slow curled stone goes over a piece in the ice which causes a lot of friction b pulling the stone and causing it to start curling the opposite way. That's what I often see. Another thing that sometimes messed with the ice and can cause negative curl is outside conditions. The building isn't perfectly sealed and there are doors to the exterior 3 feet from the outer sheets. If it's above freezing the warm air seeping in can cause the ice near the doors to be frosty or wet (or even colder than normal and harder to melt from some friction if it's extremely cold outside). Depending on conditions. This can mess with the friction between the ice and stone regardless of spin direction.

I'm not talking about picking, but more to your last point. However, I'm not sure that that still explains the exact mechanics at play.

Probably gravity. Shaving the ice in the same pattern every time, or excessive traffic on the edges of the sheet probably cause uneven surfaces over time.

Usually it's picked on something or it lost handle which may cause the rock to maybe start turning in the opposite direction. Or they just misread the call and threw the wrong turn.

I'm referring to when the rock simply curls the wrong way. Consistently, no matter who is throwing it.

It seems to be related to uneven cooling of the ice. It really becomes apparent on the southern-most sheet in the club I frequent when the late-winter sun starts beating down on the southern-facing wall next to it, but that is not the only place I have seen it happen.

However, outside of the high level reasons for it happening, I am interested in the specific mechanics, like were previously described for normal curl, that causes the rock to go the opposite way under these conditions.

As I mentioned in a different comment, it's probably just gravity. The rock slides against the curl because the ice is not level. Uneven cooling could cause the ice to freeze unevenly, or maybe even sublimate. Shaving patterns over time can also play a part.

Of course I'm speculating on the specific underlying cause, but I would be pretty surprised if the mechanic isn't just the rock sliding downhill.

A rock spinning too fast will melt more ice in front of the stones path reducing friction and lubing the ice in front and possibly pulling water over to the inside curl side leading it to fall forward more and catch less on the curl side.

P.S. This is just my speculation, not from physics but from being a curler.

Sure no problem, I curl myself :)