My question essentially is: the dyes that are in photographic film are just different chemicals that react to the silver bromide complex during development.

Undeveloped film does not contain dyes. It contains couplers. When the film is developed, the couplers react with the developer agent from the developer and dye is created. This is only happening where AgBr changes to Ag, so it only happens at the exposed places.

Is it possible to affect/target these dye chemicals specifically with the purpose of affecting their chemistry, or even replacing the dyes with different chemicals?

You can affect them a little by changing chemical composition of the color developer. This is sometimes used to fix slight color issues in process E6, for example. You can also replace the developer agent (CD3, CD4, TSS, T32, Ac60...) and/or change it's concentration in the developer, which will have impact on color.

Would it be possible to target only the "developed" dye while leaving the "undeveloped" dye intact (could be combined with using a fogging agent to produce a really strange color effect on the film).

I suppose you could target developed and undeveloped areas using the same trick as is used in slide films. There are two developers, one only develops the silver and the other, used after inversion, develops also color. Also, instead inverting all layers chemically at once, you could invert them by using light, targeting individual layers with R, G and B filters and doing development separately for each layer.