Making chord shapes up the neck sound good is very dependent on excellent intonation, and one thing that ukuleles are NOT renowned for is, excellent intonation.
So how well intonated are your instruments?
Here's something I do. I move some of the chords in the progression away from the first position but not all of them. I will often still play a baritone first position D maj (0,2,3,2 or G major with standard tuning) but then play the G major ( C major for standard tuning) at 5,4,3,3, instead of, and often as well as 0,0,0,3. I may finish a phrase at 0,0,0,3 and then start the next phrase at 5,4,3,3 , especially if the next chord in the sequence is 4,2,2,2. DO you see where this is going? Think ahead to the next chords in the phrase/sequence and pick an chord position/inversion that works/sounds best.
Often I play different positions/inversions of the exact same chord in two different positions in the same song. 0,2,3,2 is also 7,7,7,5, just different inversion G maj in standard tuning or D maj in baritone tuning.
Here's something to note if you don't already know it. The notes of the 0,2,3,2 shape in standard tuning are, G, D,G, B. In the 2nd position they are D, G, B, D. Ignoring reentrant tuning for a moment, the last/highest 3 strings from 1st position are the exact same notes in the exact same order as the first 3 notes from the second position shape. The first position shape has one lower note, the second position shape has one higher note.
In standard tuning, an A minor is commonly played as 2,0,0,0, yet it can also be played as 2,4,5,3. This is simply the standard position G minor shape, slid up the fretboard two frets. You can slide it two more frets up the fretboard and play a B minor. Then you can slide up one more fret and revert to the major triad and play a C major.
I hope I'm being clear enough.
Anyway, work out all your first position and second position major and minor chords in the same key and play around with substituting first and second position shapes in the same song.
One movement that can be particularly useful is to start on a major chord, add a minor and/or a fifth chord and then end the phrase on the major one position above.
It's a common practice in pop songs to play higher position shapes in an intro but then use the lower position shapes as an accompaniment when singing.