Taking the fifths tuning ponderings a bit further, the 4 free strings of an instrument tuned in fifths span across 21 half-steps. Reentrant ukulele strings span 9 half-steps, so tuning them an octave up and then adding the difference to the 1st string, would add up to 12+9=21 half steps, which is exactly the same span. That would mean, assuming that the fretboards (and usable notes) of an uke and a fifths-tuned instrument are of approximately equal length, one single ukulele should handle tunings with two sets of free strings spanning an octave apart!
I don't know where the usual wiggle rooms for a "standard" sized concert body would lie, but the third strings would most likely span across G3 and C4 - and then some. That is, somewhere in between C3-C4 and G3-G4. Possibly somewhere in between, and possibly containing some sweet spots.
Probably it doesn't apply to cheaper ukuleles that only take the standard tuning (and, perhaps, even the first five frets' notes or so) into account in their design, but any of the least bit ambitious designs should, one would think? I mean, there are loads of cheap mandolins, for example - do they all sound crap from, say, 7th fret and beyond?