I can only solfege (moving-do) in my head up to about Allegro 16ths at best
Congratulations. That's more than enough for most purposes. I am not sure you need more but adapting the note names to your language basic phonemes is a very good idea. Constructing a dodecaphonic version of note names is fun too. But good luck to evangelize it. I would reserve it to practice singing dodecaphonic music such as the Vienna School.
Is my ability to solfege limited by how fast I can think the syllables in my head?
Depends on what you put behind this verb, but I would say no. The basic use of solfège syllables is to help memorization and vocalization of scales, to be a support for musical notation training -- it is also convenient when discussing a musical point with another musician. When you practice an instrument you end up after some time to directly pass from the sheet-music notation to the playing action, without passing systematically through a note name intermediary. When you sing, you use the syllables of the song.
There is some notable difference in the way solfège notes are used between, say France, Italy, and anglo-saxon countries. Classical italo-french note names are taught as fixed not moving as early as their first music course. They don't do "moving-do", they don't have to transition to "fixed" letters. Most students encounter letter names much later as a weird and foreign alternative based on la instead of do and have to adjust if they want to read chords on song music written with this notation. Most musical reading material they will have will not require any knowledge of letter names. It is just fun to check the translation of piece tonalities on international sheetmusic or on CD covers. They miss the fun to play between notes and their letters, but they learn about it later if they read about Bach's fugue for instance.
Would there be any benefits to a style of chromatic solfege that doesn't suggest any diatonic aspects? Would I be better off if anything just using 7 consonants and distinguishing accidentals by vowel?
I do not think that suppressing the diatonic aspect would be a good thing. So much music is written as a mono or poly-diatonic frame of mind. It would just reverse complexity between the two aspects. This is not only about diatonic: this is also about the position of the note on the stave. If you want to modify the emphasis on diatonic, it would be logical to change the staff system as well. It has been made several times, and many softwares can display music this way.
But I agree that it is a little strange that more people have not been using a full chromatic system derived from solfege. The best version would certainly depend on the phonetic background. Some US Teachers using the movable do system extend it with vowels modifications, using "e" mainly for flat and "i" for sharp:
do di=ra re ri=me mi fa fi=se so si=le la li=te ti do
you can see that there is no place for
mi sharp, that the original
si has been renamed
ti to leave place for sol sharp =
Using the consonant/vowel opposition is not the only way. I can show you a full accidentalized version which is at least 30 years old. This is a system we played with when I was a teenager but was frowned upon by our teachers despite its qualities.
The principle is to use the (soft) z sound for sharp (= dieze in french) and the m sound for flat (=bémol in french). It's convenient because they can be prolonged as long as needed when singing.
do ré mi fa so la si do (suppressing the sol's l for homogeneity, ré and la are quite contrasted in french prononciation)
do doz=rem re rez=mim mi=fam miz=fa faz=som so soz=lam la laz=sim si=dom siz=do
C C#=Db D D#=Eb E=Fb E#=F F#=Gb G G#=Ab A A#=Bb B=Cb B#=C
It allows you to pronounce and sing uniformly any classical partition (without double accidentals) and is cumulative compared to the original note names.
Am I right in assuming that some syllables are inherently faster to pronounce than others?
Yes, but it is not strictly music, it is linguistics and phonetics. What we imperfectly write down as "sol" is not the same across languages. The troubles you have with the 'r/l' distinction is typical. Inside countries, accents can change considerably the way some sounds are pronounced.
I expect that if you practiced a system where the syllables of the solfege were strictly equal to some of the unit syllables of the hiraganas with the native accent, it would help you going faster.
Is my ability to think syllables in my head limited by how fast I can say them out loud?
Interesting and subtle question but not so easy to answer, and off-topic here I am afraid. Some people cannot read without mentally vocalizing. Some people can't even read without mumbling. So the latter would certainly be hard pressed to think those syllables faster than they can say them out loud. But the main purpose of reading music that fast is to either play it or sing it. You can easily play with your fingers faster than you can speak. And you are not singing faster than yourself, do you? Also if you practice humming when looking at a score, you can sing in your head without that phonetic limitation. I am not full capable of it but I have musician friends that are able to 'sing' chords in their head when they look at a score. And with the way they can spot a typo in orchestral sheetmusic, I believe them.
To me the overall conclusion is that you should not obsess on only one aspect of musicianship.