I am looking for simple assays to test whether large bacterial amyloid-like proteins are broken down after treatment. The solutions for testing would also contain bacterial media components.
The simplest method is SDS-PAGE with an untreated control to verify that SDS itself does not break down the amyloid fibers. This will verify fiber/not fiber, the actual oligomer species formed by breakdown cannot be assessed reliably by SDS-PAGE
SDS-PAGE would be a good option if you have an antibody against your protein of interest. The large amyloid fibrils would probably not get into the gel, but breakdown products might. You'd have to test it to see. As Jeffrey Brender says, you will need good controls.
Another option would be gel filtration (size exclusion) chromatography. A Superdex 200 or Superdex 75 column could separate large aggregates from smaller oligomers or monomer, depending on the size of each species. This method would rely on the relative abundance of your amyloid proteins (which are, presumably overexpressed) since it detects the UV absorption of all proteins, not just your protein of interest.