Better known as SEPIC. Cuk is specifically the inverting kind.
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Having played around a lot, years ago, I don't think there are any real great two-transistor no-transformer converters; with transformer, you can have a blocking oscillator with peak current mode control, which can be zener controlled for somewhat mediocre regulation. Add a 3rd transistor (as opto) for isolation.
I guess you've been feeling out those sorts of problems; the narrow voltage range and low efficiency are fairly typical in that respect, I think. Though doing it at fairly low voltage here, may be hitting efficiency more than my experiments did (mostly in the 12V range), so maybe it's not too bad, that considered.
For reference, I'd made a 1W "joule thief" with around 60% efficiency from a single 1.25V cell; which requries a coupled inductor, of course.
Speaking of coupled inductors, SEPIC/Cuk of course perform better with them; it's not required, but it helps. Not a problem for efficiency per se, you can always use bigger/better caps and inductors to account for that. It's just bulkier, so a matter of cost/size optimization at same efficiency. Which, if your components are good enough then you can discount them as loss sources, and focus on just the switching aspect, its losses.
Around 7 transistors, you can get behavior closer to something like UC3843: free-running oscillator, maybe frequency modulated, or some hybrid of fixed-on/off-time and current mode. And you can generate sharper edges, and can afford drivers for MOSFETs, netting higher efficiency.
I'm also fond of using TL431 or relatives, since, that's just one single very fancy transistor...right? RIGHT?!
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Tim