Canadian syllabics have also been used to write the Carrier (Dakelh) language; since Carrier has quite a few consonants and vowels, the system had to be extended considerably. So I had a look to see whether it was plausible to write Klingon in Carrier-style syllabics. (See part 1 for an attempt to write it in syllabics that are closer to Cree or Inuktitut.)
One piece of good news is that the phonological inventory of the Carrier language covers a fair bit of the range of Klingon sounds. For example, the vowel phonemes /i/, /u/, /e/, /o/, /a/, and /ʌ/ match fairly well to the Klingon set /ɑ/, /ɛ/, /ɪ/, /o/, /u/: just discard /ʌ/ and assign the remaining five vowels to the “obvious” Klingon equivalent.
In consonants, Carrier has a /tɬ/ phoneme just like Klingon, which is handy. It also has good matches for b t D m n ch j S gh H l y w. Of the missing consonant phonemes p q ' ng v r Q, the easiest to assign is ': this can go with the vowel-initial syllabics again. q Q could go to /kʰ/ and (ejective) /kʼ/, respectively. But there are no good equivalents for p v r, which simply don’t occur in Carrier (outside of loanwords, perhaps), and ng is essentially restricted to final position in Carrier.
Which brings up another problem: the list of possible syllable codas in Carrier is quite a bit more restricted than the list of possible onsets; of the ones Klingon needs, apparently only b D q Q n m ng l S H gh ' are attested, and while the final for /ɬ/, which Klingon doesn’t need, could conceivably be used for /tɬ/, which it does, the lack of finals for t ch j y w (not to mention p v r, which aren’t really supported at all) is not so good. I suppose I could borrow West-Cree finals for t ch y w, but that still leaves j (p v r).
So, the following is a start, but not a particularly promising one since it’s not clear how the picture could (or should) be completed:
|Consonant \ Vowel||a||e||I||o||u||Final|
(* I’ve seen contradictory information on whether the forms with the crossbar close to the angle are voiced or voiceless. The assignment here follows http://www.ydli.org/dakinfo/dulkwah.htm; for the other way around, see http://www.billposer.org/Papers/dulkwah.p
The Klingon pangram qajunpaQHeylIjmo' batlh DuSuvqang charghwI' 'It, in this system, would be ᗺᘔᐣᗭᘁᗍᕀᘦᐨᘉᐧ ᗭᒡ ᑌᙔᗮᗺᐡ ᙠᐥᗔᐧ ᐉᐟ—though due to the deficiencies in the system mentioned above, that actually represents qajunbaQHeylichmo' batlh DuSubqang chaghwI' 'It.