Doing some extra reading into the 120/240VAC single phase pump control, and it looks like the main method of controlling PSC/Shade pole motors (the typs on march/chugger/etc.) pump is using a Triac and Phase angle control....
I've been working on automating an old hotplate + stirrer and ran into a similar problem of how to variably control the speed of the AC stir plate motor. After some research is appears the best (and possibly only?) way to control most AC motors requires complicated frequency/voltage control. An exception are shaded poll motors, found in most fans (and strriers!). These can be controller via phase angle control, as mattd2 mentions. As I understand it, this trick only works with some load types. I'm not sure if a pump is similar enough to a fan to drive it correctly.
(since you want to use a zero crossing SSR that will only switch off why V=0) - so at a PWM frequency of 5Hz you would have 10% steps - going any lower/higher with the PWM frequency you would large expect surges in the pump speed or the # steps would not be enogh to control well enough....
I'm not sure burst fire control will work for a pump, it is different than phase angle control. Burst fire uses bursts of full AC sine waves, always turning on/off at the zero crossing. Phase angle control turns on the AC some time after the zero cross and off again at the next zero cross. Phase angle provides much finer control, but causes more interference (such as the whine you hear when using a cheap light dimmer). Typically phase angle control is used when a high frequency of pulsing is required, like lighting, in which we would see flicker if burst fire was used. Burst fire is used when high frequency is not required and causes less AC interference since it turns on and off at the zero cross, for example when controlling a heating element.
A zero cross SSR will not work with phase angle control, it has to be random fire (i.e. will turn on anywhere, not just at the zero cross).
I suspect if you try to control an AC pump using burst fire it will be to low a frequency to control the speed. It would probably cause the pump to either be fully on, or fully off, not some intermediate value.
I have no idea if phase angle control would work for a pump, and motors are trickier to control via triacs than lights and heating elements (inductive vs resistive loads). What you could do is buy a cheap light dimmer and see how that works, they use phase angle control. If it works, implementing phase angle control in a microcontroller is slightly complicated by the need to detect the zero cross of the AC wave, you can look up microcontrolled light dimmers for the general idea.
These problems are probably why we do not see many people controlling AC motors, since true AC speed controllers are expensive and Triac based methods are only feasible in a few situations.
