Nice implement Ross, indeed.
Now that I've had a chance to look this over closer, only one additional thing comes to mind for the "filter" question for smoothing...
The output filtration may be better looked at in terms of a "freewheeling buck converter" of sorts... there's LC action yes, but you (or anyone running across this at a later time) might find the answer to the choppy vs smoother output amongst the "continuous vs discontinuous" inductor operation associated with buck and boost converters.
In a sense, that's essentially what's taking place. When the load is sufficiently mismatched, not enough (or too much) current flows in the inductor at the output, leading to either something resembling discontinuous mode in a converter (which as you found, the cap only plays a "niche" role in), or in the case of more current than the ideal, saturation, leading to ripple caused by the core going non-linear. Tinkering with the value of the inductor will have a much more profound effect on the "quality" of the output (which of course in the case of your motor drive or other "dedicated load", can be dialed right on in.)
This isn't to say ignore the cap, it just doesn't play the role that it immediately might seem to play in the big picture.
On a related note, if you look at the front end of an active PFC circuit for switching supplies, you will spot the immediate resemblance to the final components in a PWM/PSW inverter filter... the only real difference, is (nearly literally), everything is completely reversed. The mylar cap plays a key role there just as in the inverter, and is appropriately referred to in many cases as the "resonant cap" - bigger or smaller upsets the balance of the LC and the inductor needs to be adjusted as well to suit.
Only other thing, which I'm sure goes without saying, but maybe not so much for those just starting to get their feet wet in this stuff, is of course all of this is very heavily intertwined with the base switching frequency for the PWM that ultimately creates the sine...
Ain't SMPS so much more fun than boring old iron laminate EI, a simple bridge, and electrolytics that easily found new life simply as paperweights? Or "Power Hartley's" that make better heaters than inversion circuitry?