How neat, I love the idea of a text-to-speech IPA reader. It seems that there aren't many of these, and none of them are without flaws. At first glance (and upon closer inspection), I'd say you're running up against limitations of the app.
I too, am not without my flaws, and I'll start by saying that I consider myself a mere amateur enthusiast of Japanese phonology. My knowledge on vowels is not comprehensive, and I have only passing familiarity with the superscript modifiers, so I had to do a little reading to fully understand your question.
First thing I noticed was that your links do not have the
ɯ sound (
ɾʲɨᵝː and
ɾʲʉː). To my knowledge, the end-point of ~ゅう is still the close back unrounded vowel
ɯ, and is not replaced because of the palatalization
.
In my phonology class, I was taught to transcribe
りゅう simply as
[ɾjɯː]/
[ɾʲɯː], and that the palatalization naturally creates the transitory high(er) vowel sound through assimilation. It starts at the flap, where your tongue contacts the alveolar ridge, and as your tongue moves towards
ɯ there are what could be described as intermediate sounds. Saying it to myself I can hear what you mean about "fronting" as the palatalization leads into the final vowel sound, making it sound sort of like a dipthong. I'm not sure if it's possible to properly pronounce the palatalization without the assimilation, so transcribing the fronting sound seems unnecessary to me personally; ultimately you will have to make the higher vowel on your way to the
う as a matter of physiology.
I also noticed that if you change the "voice," some of them do a better job with certain sounds (try the french, spanish, and tatyana (russian) voices), but to recreate
りゅう,
きゅう or
ちゅう it's necessary to spell out the transition as
ɨɯ, and the superscripts, palatalization and long vowel markers don't seem to matter: you can remove these characters and play again, and notice that the sound doesn't change between
ɾʲɨᵝɯː,
ɾʲɨɯː,
ɾʲɨɯ, and
ɾɨɯ... Mizuki does not handle these sounds well though.
As I was just doing this, I found it interesting to repeat ゆう to myself, then introduce the flap and make it りゅう, and notice the subtle differences, mostly in the tongue's position. As an experiment, change the voice to Tatyana (because this doesn't work with Mizuki) and test
jɯː and
ɾjɯː. Yet I see that if you enter
ɾʲɯː, the palatalization disappears and it sounds the same as
ɾɯː (this seems like an error to me)
I would chalk all this up to limitations of the tool (which was likely created from audio clips and not a computer model of the human vocal tract), and I'd say that it's probably not super helpful for accurately testing your transcriptions. It may actually be counter-productive if it forces you to use these unusual character combinations in order to get the voice to behave.
edit: added links to make things easier and save the trouble of copy-pasting.