Since you are married to a Chinese woman, you can get a China visa good for a year with NO requirement to exit China during the visa period. You need to get a certificate showing no crimes from the local Police Department, have your marriage books in hand, then go to the visa office. Cost is about 600 RMB.
As far as proving the marriage is legitimate, living together is probably the best and perhaps the only proof, given that you married so quickly.
Ignore the lectures about whether your wife is honestly in love with you or not -- no one can really know that except her. But the VO must be conservative and consider the possibility. So, forget an appeal at this stage; it would probably fail. Use the money you'd pay a lawyer to spend time with her -- either lots of time living together in China or several visits to see her (for maybe a month or two at a time, if possible) . Then try your application again.
How much time to spend together before re-applying? The longer the better. Ask a few immigration lawyers. I suspect that three months is not long enough -- despite the laws about common-law relationships in B.C. They don't apply; you are dealing with CIC and arbitrary VOs who can decide what they want, with apparently little accountability. So the longer the better.
One proof of a relationship would be certified letters from neighbours saying that you have spent X amount of time together. Let the letters be specific about how much time together. If getting the letters notarized is too much effort (it can be a real trial in China, I know), then at least have the neighbours provide contact information, and invite CIC to contact them for verification. Letters from family members would have less credibility than letters from objective neighbours.
Good luck, and welcome to the world of international rules and regulations! :-(