Ooh, this could get complicated.
Hopefully you can figure this out soon, but losing the passport as well kinda takes a PRTD out of the picture until you can get a replacement passport issued.
1. No idea about the SJTD and airlines/airport question. Never heard of this before, but searching for it mainly comes up with refugee or stateless person situations - have you confirmed this is an option for you ?
2. Just thinking out loud here in case the SJTD doesn't work out for ya. Can someone in Canada scan the documents you need and send you the PDFs ? - I don't know the replacement process for a lost Indian passport, but this might work if the process is entirely online ?
Then get a PRTD after that. Obviously all this will mean you won't be able to fly back to Canada for a while.
Also, when you lose a passport, i believe you need to file a police report and report it to the the relevant authorities or something like that - i would check if you need to do this. Maybe a police report will help you get a re-issued passport without having the physical documents on hand or help reduce the processing timeline ?