Ukulele intonation

[Stray Feathers]

I finished my tenor ukulele triplets (thread in the "Blog Your Project" section) and after getting used to them (I haven't played ukulele) I am finding that some fretted notes play out of tune. I used scale length from the Hana Lima 'Ia book and plans, for 12-fret ukes. Saddles are perpendicular to the centre line. Notes fretted at the 12th fret are sharp compared to the harmonics on all strings. I tried compensating one of the saddles as I would a guitar, but it seemed to make little difference, and I have run out of room to compensate further. I lowered the action at the first fret to near .5 mm and 2.5 mm at the 12th fret, but they might go a little lower. I can offset the problem some by tuning so the worst strings are slightly flat when open, and okay in a G chord say, and that works not badly. I am wondering if I should have made the scale a fraction longer to begin with (i.e more than twice the distance from nut to 12th fret)? Could I replace the existing saddles with modified (thicker) versions to slightly extend the scale length and allow for a bit of compensation? I don't have a lot of ukes accessible to see what is "normal". There is also this old post by John Parchem which I did not fully understand:

viewtopic.php?f=7&t=7019&p=36546&hilit= ... ion#p36546

And finally, thinking as I write, maybe I should not try to intonate for perfection at the 12th fret (where I will never play) and compensate to make the high strings shorter and the low strings longer? The existing saddles would allow a little more compensation that way I think.

Any insight for a new uke builder appreciated - Bruce W.