Coming from classical guitar, prior to getting into ukulele, I had purchased a Yamaha GL-1 guitalele.
Once the shiny wore off from being new, I realized that the nut width of 45mm was WAY too tight compared to the 51mm of my full size classical, but I still have it. I consider it 'replaced' with the Cordoba Mini SM-CE (spalted maple back and sides (lam), cedar top (solid) and pickup/preamp).
Since getting into 5ths tunings, and having several instruments strung this way, I have considered hacking the GL-1 to be a 5-string instrument, tuned in 5ths F2-C3-G3-D4-A4, but currently lack the time to make the modifications to the nut an bridge...
I have also been looking at some of the other instruments mentioned at the top of the thread, primarily those that are built for steel strings, so as to have a 4-course, 4-string instrument to tune in 5ths like a mandolin, G3-D4-A4-E5, but with a much more comfortable nut with and string spread and only 4 strings instead of the 8 of a mandolin.
I tried a few mandolins in the local music shop, and found the 30mm nut and 28mm string spread near impossible to play compared to my custom tenor guitar with a 42mm nut and 38mm string spread, so a steel-string soprano uke cousin would be great...but they are all considered 'exotic' or niche instruments here in the USA and most are selling for about 3-4x of what I'd be willing to spend...
I also have a Lanikai LU-21B baritone uke tuned in 5ths G2-D3-A3-E4, and a mango tenor Fluke tuned in 5ths, but re-entrant, as C4-G3-D4-A4.
So whether these are mando-style or some alien world of 5ths tuning, they are still ukes in construction, but with different string configurations.
I spend about equal time in 5th tunings, and uke tunings, as well as with the Cordoba Mini, which is in fact in Terz tuning, G2-C3-F3-Bb3-D4-G4, which is similar to the ukulele Bb tuning, and Terz as the name is derived from the Italian word meaning 'third' as in 'a minor third up from E tuning' and there's a significant amount of classical music written specifically for Terz guitars from the Medieval, Renaissance and Baroque periods, but I use it mainly for my own songwriting....