I know of one Islamabad case similar to yours where the child was in Canada on a TRP (because the TRV was rejected due to the visa officer deciding the child would not leave Canada at the end of the visit and was thus inadmissible). The TRP (H&C basis) overcame the finding of inadmissibility.
That person kept CIC updated on changes in address but CIC Islamabad decided to send a letter to a very old address (one that was not used by CIC Vegreville when the child's TRP was renewed again, for example) and the letter never reached the sponsor. CIC Islamabad sent a second letter (same address) and then finally sent a refusal of the application - after the three year wait. The sponsor finally received the refusal letter six months after it was first sent. He was trying to decide if he should challenge the refusal OR request that Islamabad reopen the file OR apply again. I pointed out that any of these options was likely to take more than 2 years - at which point the child would have been in Canada on a TRP for five years and would automatically qualify for permanent residency in the "permit holder's class" (try finding the forms on the CIC website - they are there, but you have to know they exist to find them in a search). That special class gives CIC little ability to refuse the applicant: it has to be medical or criminal grounds not previously raised.
So my point: get the child into Canada on a TRV or failing that on a TRP. Once here, you don't care how long it takes CIC Islamabad to process that application. Just keep the TRV/TRP renewed and you'll be fine (TRP is actually better usually because it makes getting health care easier).
I agree that the Islamabad processing times are discouragingly long. I suspect it's not considered an ideal post abroad, so positions are difficult to fill and do not attract the best and brightest.
