Forget about official websites, what matters is actual practice in real-time, which may or may not deviate.

OP, best Options, each with pros and cons.

1) Assume that in Canada, the best you can hope for is a single-entry or a double-entry, for which you will pay the US$140 or equivalent. Worst visa terms but least hassle and least cost, as you can do upon your return from SF without Rush Processing. Be aware that you will normally have 90 days to get to a border and activate the single entry, usually 180 days for the double-entry. So if your RTW isn't soon, don't apply too early.

2) You can take both passports and apply at the SF Consulate when you are there. Inquire ahead as to what their fastest time frame is. If it meets your own time limitations in SF, go ahead and pay for Rush Processing on top of regular $140 fee. You will likely have no problem getting a multiple-entry visa good for 12 months, I'd give chance at >75%. Worst case, you'd likely be knocked back to double-entry. If you can, put down a US address on the application but don't stress out too much about this. For the 12 month multiple, there is no time limit on initial activation as long as you enter within the 12 month period.

3) Use a visa agent. Once back in Canada after SF trip, send the passports with application stuff to www.mychinavisa.com. I use the Houston office but I think they now have a Chicago office. It doesn't matter. You will certainly nearly 100% get 12 month, multiple-entry visas this way and you can use your Canadian address. It will cost more, std visa fee + agent fee + FedEx fees. Turn around to get passport back in your hands is generally 10 days using standard non-Rush.

4) Play it by ear and just get the Chinese visa in HKG. Can be done with next-day delivery. Single entry for 30 days always available, sometimes longer periods and sometimes double-entry or more, but don't count on the latter. You will still pay the $140 equivalent in visa fee, + a little more if you use an agent like Forever Bright (recommended).

You are getting ahead of yourself, though. You need to go back and reassess your plans. I can't fathom why anybody in your shoes would be planning to make day trips back and forth from HKG to Shenzhen. If it's for shopping, don't bother. And there's nothing else in Shenzhen, it's a pit. If you want to see China, dammit, just go there rather than do multiple half-@ssed border skirmishes. For which you wouldn't need anything more than a single-entry. If you plan to--within a 12 month period--return to China beyond this RTW, then it makes sense to do the 12 month multiple. Or you could just save yourself the entire expense of the visa on this trip, and just plan to not go into China.

If your time in HKG is so long that you will exhaust your possibilities for activities there and in Macau, and you also don't want to really see much of China, then you should cut down the overall time in HKG and move to the next point faster on your RTW, rather than trolling about for daytrips.