Ottawa may be fastest and not as complicated as NY/LA if you could get a prepaid courier envelope to ship back to you.
I don’t think IRCC is to blame but those third parties you suggested.
Yeah, after reading their weird instructions, I do not understand why anyone would send to the VAC. There's an uncontrolled element of mailing there (and I'm sure they'll choose the slowest, most unreliable option just to increase delays, probably with a tip to the mailman to dump it in the river - are they scored on how to delay applications the most?).
At least with Ottawa I control the mailing aspect and use the fastest option and with close tracking. Also in the past they usually didn't keep it for far too long (though not sure if this helps anymore....before visas used to take 10 days and here I am, about to hit 3 months...)
The blame for delay is mostly on IRCC in the first place because this particular application should have been a direct slam dunk. They wasted a lot of their time & resources & most importantly mine, completely unnecessarily, both on security or overstaying grounds. I would share details if I weren't worried about anonymity.
For comparison: US visas are awesome. You get the decision ON THE SPOT in the interview, they grant years and years, and they keep the passport and mail it in THREE DAYS!! They also don't ask you to spend hours filling in your parents info again and again, etc, or travel history for the freaking past 10 years. (And of course on IRCC's end there's an employee typing all that crap in, taking ages).