I don't know anything about the physics, but here's something field-related that seems particle-like to me. On a smooth manifold (which is a space that is "locally Euclidean" in such a way that you can do calculus), there is a concept of a smooth vector field, which is a smooth assignment of a vector tangent to the manifold to each point. While there isn't too much to constrain a vector field, there is an invariant: if you take all the places where the vector field vanishes and compute something called the "index" there, and sum up all the indices, you get the Euler characteristic of the manifold. Index is an integer quantity, and it roughly corresponds to how many times the vector field spins around while going around the vanishing point once.

You can smoothly deform vector fields through time, and there are different features you can notice: zeros of opposite index annihilating each other, zeros of opposite index appearing out of nowhere, and other sorts of combinations of zeros combining and splitting.

For the surface of a ball, the Euler characteristic is 2, so the sum of indices must be two, so it seems spheres must be "positively charged," if index and charge are actually analogous. For a torus, the Euler characteristic is 0, so the "charge" is neutral. For a plane, on the other hand, the theorem I mentioned doesn't quite work because it requires a compact manifold, but a vector field could have any total index (though there will be a virtual zero at infinity which always has the opposite index).

If measuring charge corresponds to finding the total index in a region of space, then maybe that's why it's only ever an integer.