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I'm trying my first wash, using a package of Super X-Press yeast, 8 kg white sugar, and 22 L of bottled spring water (I don't have a 30 L bucket, and I was given some winemaking supplies including smaller (25 L?) buckets). I realize this is pushing it a bit, but I was also hoping the smaller water volume than recommended would speed up the process a bit as the yeast package says 5-7 days for 20% abv - 5 days would be ideal for me right now.

I started this yesterday morning. I checked it after about 1 hr and again after 2 hrs - it seemed to be fermenting vigorously as a yeast "head" had developed during that time. However, I checked it again after about 12 hrs, and the yeast head was no longer there. Is this normal? I still get a "fizzing" noise from the bucket which is similar to the fruit juices I have fermented in the past, and I left it overnight and the fizzing still continues (if I stir it the fizzing gets louder temporarily). The air temp. has been a steady 77-78 degrees Fahrenheit, and the wash temp. is currently 81 degrees F. Definite "yeasty" and alcohol smells coming from the bucket. Unfortunately I don't have a hydrometer to measure SG, but I will be getting one shortly.

So, is it safe to assume it is still fermenting as it is fizzing? Should there still be a yeast head? I'm a bit paranoid about the wash stopping/stalling unexpectedly...

you sort of got it backwards, the more sugar per the amount of water the slower it will ferment,each time you double the sugar you increase the ferment time by 3 ..this also increases the chance of stalling,off flavors .. your not totally blind with out a hydrometer, when it quits bubbling/fizzing and taste "dry" like dry wine it is done,then let yeast settle to bottom,siphon off the clear.I doubt very much if it will finish in 5 days,more like two weeks.
going back to the amount of sugar,,, you can make 10% wash in 1/3 the time you can a 20% wash,so you can make 3X the amount in less time and have a better product.

Thanks - in my head I assumed the yeast would "go nuts" and work faster if there was more sugar-to-water available, but I see that assumption is incorrect.

I do have another bucket available - now that the original has started fermenting, if I stirred it up and transferred half into the other bucket and diluted both buckets, would I potentially end up with 10% abv in each bucket? Would I have to add more yeast to make that work properly (I can get champagne yeast easily here)?

a good idea, you should not need more of anything but water. just stir it/split it and add water then it will finish much sooner.
you do not have to measure, just estimate,that will be close enough.