How can I isolate a power well to reduce noise
The current transients mentioned, depending on magnitude and how well the amplifier circuit is decoupled, may cause dips in Vsupply as described.

Some points to address for a solution:


Most important: Use a freewheeling diode, connected reverse biased, across the speaker leads. The on-to-off transition of the speaker causes a significant reverse spike from an inductive load such as a speaker.

Use a power Shottky diode if the current involved is big, else any fast diode with a current rating of at least twice the current expected through the speaker coils in on state would work.

Use a lot of bulk capacitance at the source of the transients, i.e. across the amplifier circuit, to reduce supply noise propagation: One always tries to eliminate noise at source if possible. 

Depending on the transient magnitudes, a few hundred to a few thousand microfarads are common in power audio amplifiers. Voltage rating of better than twice the supply voltage would be best.

Separate out the power and ground planes for the amplifier portion and the microcontroller portion if feasible, interconnecting grounds at a single point.
Coupling the power plane using a choke coil as mentioned in the question is a good additional measure, but ensure this is a very low resistance high inductance coil, preferably with a core. Tricks with PCB traces will not provide the high inductance needed, an actual inductor would be best.

Values from a few hundred microHenries to a milliHenry or so should be good to effectively throttle spike propagation. Use an inductor with the least DC resistance that you can afford. Personal preference is something well under 250 milliOhms if possible.