Generally speaking, you want to apply for a TRV before submitting a conjugal application. But of course this is your choice. If your partner can get a TRV approved, then you can either get married in Canada or can live here together for a full year to become common law (then you can sponsor your partner as either your spouse or common law partner). We have seen issues with conjugal applications on this forum where the person being sponsored has not tried to apply for a TRV before submitting the conjugal application. But again, your choice.
IRCC is quite strict with their rules regarding common law relationships. Keep in mind that when you applied for PR in Canada, you did this under Canada's rules (not the rules of your home country). The fact you were common law before you came to Canada but you didn't include your partner in your application is a big issue from Canada's perspective. Again, I think you are very wise to be working with a good lawyer. Good luck and let us know how it goes.