Are TVS diodes a good mechanism to reduce specific kinds of electrical noise?
Your ideas of adding TVS diodes and caps close to the ESCs is totally correct and exactly what I would have suggested.
1) make sure your TVS diodes can handle the power dissipation of all your spikes, so choose a big package to avoid thermal issues, like 5KP20CA. This is also a bidirectional type, because your system is battery driven, so you do not have a solid potential.
2) In my option the 1000uF cap is not necessary, use two 220uF in parallel instead. Thus you can lower the ESR even more (parallel resistors)

Of course you can add a real L-C-filter before each ESC, but I don't think this is necessary.

Update: There is no need for a bidirectinal TVS diode, just use an unidirectional one. Srry for the confusions. I looked up, which type can be used with 18V Reverse Stand-Off. The results showed that the breakdown voltage is normally at 21.1V and the Clamping Voltage is 29.2V, like for SMC30J18A > Farnell Filter. Thus you should higher the max. voltage of your caps to 30V or 35V.