Since you don't seem to have many red flags, I would suggest you apply outland, and then apply for a visitor visa for your wife. Of course there's a higher than normal chance of rejection, but you really have nothing to lose by applying. Note that if you apply for both the TRV and sponsorship, you should submit as many documents and evidence as possible to improve the processing time and chance of success.
My wife got her TRV while married to me and had a spnsorship file pending, and she got a multiple entry TRV for the life of her passport(see my signature). Both her country (Vietnam) and your wife's are deemed high risk overstay countries that require biometrics, so yeah both parties would have a harder time getting a TRV than most for sure.
I just noticed that you're a PR, not a citizen. In which case, you're supposed to remain in Canada in order to sponsor.