FAA to TCCA is not the only method, but it is the easiest.
The Foreign License Validation Certificate is what everyone else uses. It's a process though. What you need to do is compare your experience against the Canadian equivalents through
CAR 421. You must then make up any hours you are short on before applying for the conversion, or they just convert you to one license down - so if you hold an ATP but you are 5 hours short on night time, then you will only be awarded a CPL (assuming you meet those requirements). When I say everything must be met, I mean
everything. You could have 1000 hours of night PIC, but if you're short 3 hours of dual instruction at night, you're going to have to make that up. I would strongly suggest, however, that you simply do the license itself as I cannot recall if you can move up to the next stage of license if you converted via FLVC - that you can ask Transport Canada directly. Speaking of, license conversions are only done by Transport Canada - while there are schools that can prepare you for some of the additional training or exams, you want to go directly to TC first. You may find you save a bit of money.
As for getting a job with a work permit. Yes, you can. That's the whole point of the work permit. There are so many opportunities right now at the smaller operators that I'm sure you'd find a job, not a problem. Air Canada and WestJet, probably not. I strongly suggest you temper your expectations when you come here though. If you're currently flying a 737 or 320, there is a good chance you won't be when you come here; not at first. Expect something like a King Air or Beech 1900D. I'm not saying it can't happen, but I've experienced a lot of guys who came to Canada having flown 777s or 747s and suddenly they're back in the right seat of a King Air or Q400 and their ego can't handle it. Come in with a healthy check of your ego and you'll be OK.
Finally, expect 40 business days for your medical. It's my experience that they prioritize working pilots over applicants, so it might take longer than that. Add on another 10-20 days for the license certificate.