Seemingly, if one is ahead of the congregation and reaches "Yishtabach", he should recite it. Now, suppose he does so, and then the fellow in charge of getting people to lead the services comes over to him and asks him to lead shacharis. (Assume for the purposes of this question that he cannot, or does not, refuse, and goes to the lectern to lead the services.) Normally, the shacharis leader starts reciting aloud from "Yishtabach" and then says kadish — but, of course, in this case, he's said "Yishtabach" already. Skipping reciting it aloud will be unusual for the congregation (not a big deal necessarily) and may cause someone present who cannot himself pray to miss out on hearing a prayer and fulfilling his obligation that way (not likely, but conceivable, in most synagogues). On the other hand, I seem to recall a rule that no one say chatzi kadish between prayer sections without saying the preceding prayer immediately beforehand; if I recall that rule correctly, then for our protagonist to start with kadish would be inappropriate also. So what should he do?
Rama discusses a similar situation in ShA OC 54:3 where, after reciting Yishtabach, the congregation halted the prayer service for specific Mitzva/communal needs. He recommends in that case for the Chazzan to recite "some verses from Pesukei Dizimra" and say Kaddish "on them". (It seems to me that his specification of "from Pesukei Dizimra" is lav davka and any verses should suffice, though those may be thematically appropriate.)
Regarding your first point: I am not aware of an obligation on the Chazzan to fulfill illiterate congregants' obligation to say Yishtabach. Indeed it seems unlikely that there is one, as traditionally there is no mandated Chazzan for Yishtabach's sister-blessing of Baruch SheAmar (cf. ShA OC 53:1 who begins the Chazzan's role with Yishtabach). Furthermore, Rambam in his presentation of public prayer (Tefilla 9:1) omits the public recitation of Yishtabach entirely.