Then you have a problem with the original suggestion by Wheeler/Feynman that the article in the OP describes, because that's what it describes.

The image in my mind is the vibrating, twisty path /out there/, not necessarily in spacetime.

"Out there" is spacetime. Spacetime is what the twisty path exists in.

Through this path passes a continuous surface that could be be thought of as the 'current moment' of our observable reality.

Each such "current moment" is a spacelike slice through spacetime.

Each crossing/intersection of the electron path through this surface would result in an observable electron.

More precisely, it would result in a single observation of "the" electron, since in this model there is only one electron--but it crosses the same spacelike surface multiple times, and each crossing results in a separate, distinct observation that, to the observers, looks like a separate electron.

This would then result in the 'single electron' being be the intersection of a uniform diameter path along the reality surface.

No, the "single electron" is the twisty path through spacetime--or, if you give it a nonzero spatial size, it's a twisty "tube" through spacetime. See below.

google shows that electrons have a physical radius

There are a lot of technicalities surrounding this, but it will do for this discussion.

I'm having a hard time coming up with any way that these intersection points would have a spin.

Actually, it's easier to see how an object with a finite radius could have a spin: just think of it as a spinning ball with that radius. (There are technicalities here too, but they don't really matter for this discussion.) If you think of the electron in its entirety as a twisty "tube" through spacetime, the electron's spin is just an extra twist to the tube: in addition to the tube itself bending, its surface twists like a barber pole. The intersection of this with a particular spacelike slice through spacetime would make the barber pole twist appear as a measured spin.

It's harder to see how a point with exactly zero radius could have a spin: how can a single point spin?

What would be the appearance of the electron in your model?

See above.

I couldn't see it being what we would call an electron travelling along this spacetime path because it would have a need to be in multiple places at the same time

Traveling along a spacetime path that bends is exactly what enables it to be in multiple places at the same time. Being in multiple places at the same time just means that the electron's world-tube through spacetime bends around so that it intersects the same spacelike slice multiple times, as above.

I'm also seeing a problem of names, where 'the electron' and 'the twisty path' are being used interchangeably, but we're also talking about 'an electron' and 'the electrons' that exist on the reality surface. It gets confusing :)

I can see the 'barber shop twist' as being able to provide the necessary spin, but I'm not seeing how a sperical radius can come about from a slice along a path; a circular diameter yes, but a spherical radius is escaping me, unless the slicing 'leaks' energy (or harmony) to create some filling space around the intersection.

Nice discussion, but the indentation level is getting deep. Continue over email? Mine is in my profile if you're interested.

This depends on how "spacetime" is defined, which, as far as I can tell, depends on who is doing the defining. I've seen some papers where the word "spacetime" is applied to the full 10- or 11-dimensional manifold on which string theory (more precisely, superstring theory) is done; I've seen others which carefully use "spacetime" only to apply to the 3+1 manifold we actually observe, and use other terms like "internal symmetries" to describe the other dimensions.

That said, I think there is a more fundamental issue with a model which says there is only one electron and it moves in a twisty path through all 10 or 11 dimensions instead of just 4. (I see you actually had in mind a model with the twisty path not including the time dimension; that won't work either, see below.) Such a model could be constructed, but in order to compare it with experiment, it would have to make predictions involving only the 4 dimensions (3 space + 1 time) that we actually observe. In other words, whatever is happening in the other dimensions would have to boil down to determining the numbers or coefficients that appear in the ordinary 3+1 dimensions, things like the mass and charge of the electron; we have no way to actually observe "movement" in the other dimensions, and we certainly do observe electrons moving in the 3+1 dimensions, so the only predictions we can test are predictions about movement in the 3+1 dimensions, and other things like the mass and charge of the electron that we can measure in 3+1 dimensions.

In other words: any model that says "there is only one electron" has to include that one electron following a twisty path in the 3+1 dimensions we observe, regardless of what it says about the electron's path in other dimensions. And whatever it says about the electron's path in other dimensions can't be tested experimentally anyway, except if it makes predictions about numbers like the mass and charge of the electron that we can measure.

My argument is based on the twisty path moving through n dimensions (including the first 3) and not necessarily through the +1 of time.

Time has to be included, because we observe electrons at different times. A twisty path that didn't move through the time dimension would predict that we would only observe electrons at one single instant, and then they would all vanish (because the single electron underlying all those observations doesn't move through the time dimension).

I'm not seeing how a sperical radius can come about from a slice along a path

Remember that the "slice" is 3-dimensional. When you are imagining a circular slice, you're imagining a 2-dimensional slice. The 3-dimensional analogue of that is a spherical slice; in other words, the intersection of a 3-dimensional slice out of spacetime with the twisty tube that is the electron is a sphere.