I have tuned my D-VI E to E, using classical guitar strings. It is based on a tenor scale. It does work, but the tension is too low to be comfortable.
There are string sets that are set up for a 19" scale length.
G to G is another tuning, you can try.
I keep coming back to A to A because it is not E to E. You can deal with it at several ways:
1. You can play it as a transposing instrument using guitar arrangements that will sound a fifth interval higher.
2. You can play it just like your GCEA uke without touching the low strings.
3. You can play it A to A, with the middle C at fret 5 of the G string and the open C string, which is a C4 note. This moves the centre of gravity of the music to get a completely different voicing to what you get on a guitar. And allows you to put some of the treble parts into the low ADG strings, which you might not do on a guitar.
4. You can play it A to A, with the middle C at fret 3 of the low A string. This is a C3 note and moves the music down a whole octave. Giving another voicing option for your music. So you might play most of a tune on the ADGC strings and leave the high E and A alone altogether, sort of the reverse to playing a tune on a guitar on the DGBE strings. Because it is ADGC, it does not sound too low.
So I think keeping the piccolo guitar or guitarlele in A to A tuning is better than trying to tune it E to E, it is voiced in a higher part of the musical note range, much closer to human voice than the E to E, and offers some interesting voicings and options if you take the time to arrange the music to take advantage of the voicings.