I don't see ukulele topics very often on HN, thanks for posting!
I'm a uke player and I have an "octave ukulele" too. If anyone is curious to try this out themselves, here's a link to the strings I use on mine (they're called Perry's Octave Ukulele Strings). You just put them on a baritone uke and tune them to (low)GCEA. They are great strings: https://starlightukes.com/product/776499
I must admit, I don't think the octave ukulele sounds that much like a cello, but I see you only said it sounds a "little" like a cello, and I get what you mean with it being a deeper sound :).
Speaking of 4(ish)-stringed instruments, the mandolin family has a whole set of instruments corresponding to all the orchestral strings. The common mandolin having a tuning identical to the violin, the mandola down a fifth with tuning matching the viola, the mandocello down an octave from the mandola to match the cello and the mandobass, like its orchestral cousin tuned in fourths EADG (this last is also the only one of the mandolin orchestra instruments to not have doubled strings in each course, although other mandolin family instruments have single strings in each course.
It sounds nice, and I like it more than a regular ukulele. But I remain unconvinced: I still haven't heard anything at beautiful or mesmerizing at the sound of Cello.