Again, don't know that anyone has used them this way, no idea whether the relevant agencies would accept.
OHIP: your old one is no good.
SIN: complicated - if inactive (or so-called 'dormant' status), it's a bit complicated. The number is good and can be used to work. The dormant status was introduced to reduce risk fo fraud and access by other parties (eg fraudulent access to benefits). Service Canada seems to require PR card, current. In my view there is no legal basis for that - compliance with residency obligation has nothign to do with PR's right to work. (And after all, Service Canada or CRA or whatever other department could ask this of IRCC directly, and not put the onus on the PR). BUT: would need to be challenged, legally.
And note: even though employers could be contacted, the PR-out-of-compliance is working legally. Now, a lot of employers don't like dealing with questions from CRA - but in my view about the only thing they could ask of the employer is to confirm identity. (Also why I asked above: there's very little information about what CRA does actually ask about, or if they even do. And some unsupported claims about this)
Again though: I think SIN is the least of the potential problems, which are daunting and numerous.