Well, technically my 90 days of tourist visa is up. The official from informes@migraciones replied to my email last week (before my 90 days expired) telling me the following:
Es menester indicar que, de fecha 19 de marzo de 2020, la Superintendencia Nacional de Migraciones emite la RESOLUCIÓN DE SUPERINTENDENCIA N°000104-2020, que establece la suspensión de los plazos administrativos y la multa por exceso de permanencia, asimismo, en el artículo 5° de dicha Resolución, se establece que la vigencia de la calidad migratoria (en su caso, la de turista) se extienda hasta el levantamiento del estado de emergencia nacional.
So my tourist visa stays valid until whenever they lift the estado de emergencia, so disregard the 90 days - it doesn't matter - and I guess that also explains why the Prorroga de Permanencia tramite is disabled on their agencia virtual. Unfortunately, also in the same breath, they absolve themselves of any responsibility to respond to the residency petitions within their previous administrative time frame of 60 working days.
I was intending to buy some land in the next month or so with my wife, now the notary won't let us, because I can't get the Permiso Especial para firmar contratos either, because that tramite indeed follows the 90-day visa limit even though we're supposed to disregard the 90 days because of the estado de emergencia.??? My wife's DNI says "casada," so in order to legally sign over a land title, both spouses must sign. Unfortunately without the Permiso Especial para Firmar Contratos, I won't be able to participate. Unless of course the notary somehow finds a way (legal or not) to eliminate this requirement.
This situation is pretty wild, and also wildly inconvenient. Logically speaking, I can't see how the current situation prevents an overpaid government keyboard jockey from hitting the OK button on my residency application. There have been no requests for subsanacion, no messages whatsoever delivered to the internal buzon electronico. What's the hold up. I guess there must be a million foreigners that entered Peru between March and September this year, despite the travel ban, so they're just too inundated from all the residency applications. Yeah that makes sense! Not.
It took me one day for me to successfully submit my application with all the document scans, but it's taking them over 90 days to respond to it.