22" is close to 560 mm's. That scale length sits more comfortably in Terz tuning ( in G). Indeed historical Terz Guitars (Gut strung) have string lengths at or close to 560 mm's.
If we were to tune it to standard Guitar tuning and accept 6 Kg string tension then the G string would work out at 1,25 mm's diameter (in Nylon). At 7 Kg string tension (modern Classical Guitar tension) the diameter would be 1.35 mm's. Both of these string diameters are rather chunky for an unwound, plain nylon string.
Drop to 5 Kg string tension and the diameter goes down to 1.2 mm's. Swap this string with a pure Gut string (higher density) and our G string, at 5 Kg, will drop to 1.0 mm. Go to a Carbon string (even higher density) and our 'G' is at a very low 0.85 mm diameter.
That shows the relationship between the pitch, string length, string density (the material), string tension and the resultant string diameter.
It's quite obvious that heavier strings (higher density) result in :
a. Higher tension
b. a thinner resulting diameter.
All the other parameters remaining constant.
And that is why the lower 3 strings on a Guitar are virtually always wound with metal. The metal effectively increases the strings density - and by a huge margin.
So let's take the example of the low 'E' on a nylon strung Classical Guitar, pitched at 440 Hz. The low 'E' lies in the C-B octave range, producing a frequency of some 82 Hz. 650 mm is 'standard' string length. Near 7 Kg's is 'standard' string tension for these guitars.
That produces a plain Nylon string of 2.75 mm's in diameter. That's more like rope! and would sound rather clunky and slow. We are stuck with the scale length, the pitch and the string tension we want to play at, The only way we can significantly reduce the diameter (in this example) is to increase the string density by introducing a metal wound string. As soon as we do this the string diameter changes from our hefty 2.75 mm's right down to 1.2 mm's. It no longer feels like rope.
That is also why Ukes rarely need wound strings: much higher pitch, much shorter string length and lower string tension all make the wound strings unecessary.
So the logical solution for the OP, and assuming standard Guitar tuning, is to drop to string tension of around 5 Kg's. The downside is that you lose a little volume. The advantage is that it's a little easier to play.
Either that or pitch the instrument higher.