I'll answer this for you while we are waiting on Headmaster Ken.
I think you are proceeding with China EFL employment in the riskiest way possible: Fly to China on a tourist visa to look for work with a fake degree then figure out how to--hopefully--convert this tourist visa into a work visa and pray the entire time that no one questions this digital copy of the fake degree and asks you to present an accompanying transcript or the original diploma and transcript. That's a lot of "ifs," "hopes," and finger crossing.
Whether or not you can pick up a Z-visa in Hong Kong or a nearby Asian country depends entirely on the city, province, and school type. Virtually all universities will require that you return to Canada. Some private schools will have enough guanxi (pull) with the local police to convert this L-visa to a work visa, while others will tell you that you'll need to head off to Hong Kong.
We don't recommend this approach at all. At the end of the day, the chances are great that you will have to return home to apply for the Z-visa or continue to work in China illegally for the entire duration of your stay. Many schools will tell you that they can convert that tourist visa into a work visa and then will leave you hanging indefinitely. Have you read the various horror stories of such empty promises on these forums?
You don't need a fake degree to work at most private schools. While you will be able to successfully satisfy the hiring needs of most Chinese private school owners with a Photoshop'd diploma (primarily because they truly don't care), you won't be able to fool other foreigners who happen to have a real degree and know the difference in education when they see it (via subtle to major differences in self-schema, self-expression, vocabulary, critical thinking, style of persuasion, etc.). You'll have to be forever careful about whom you befriend because you'll be living and working there with a big secret.
To answer your question directly, the process for applying for a Z-visa is the same whether you do it from home initially or after a return flight: your papers will not be scrutinized more closely in China because you had to fly back to Canada a second time. A three-month dual- or multiple-entry visa means you can stay in China the entire length of time without ever leaving.
If all the stars and planets happen to be aligned in just the right way, you may be able to pull all this off without major difficulties, but this is not the safest way to proceed, certainly not with a husband and child in tow. Especially with nine years of Asian teaching experience and a TESOL certificate, again, there are plenty of private schools in China that will hire you without a college degree.
PS. I strongly encourage you to stay away from the anonymous China EFL forums for the distinct purpose of obtaining important information. Anonymous posters can and do write anything that tickles their fancy. Most of what you read is sheer nonsense and some of it is even deliberately misleading (from Western lackeys of Chinese school owners). Anonymous China forums are fine for virtual socializing and learning where to buy Western foods and that's about it. Be careful.