This will be difficult to pull off for 5+ years (these days the wait for spouses of PRs is about 5 years + processing time). Your wife will risk losing her green card. She can visit you for a few months each year. But if she lives with you and goes to the USA only for short intervals, there's a good chance she'll lose her green card.
Another approach you should consider is for your wife to settle in Seattle and you in Vancouver. Becoming a Canadian landed immigrant (PR) may be easy if you have the points, which you can accumulate via education + work experience + English. Citizenship and Immigration Canada has a
test you can use to compute your points. Also check the Canadian processing times for your region - some seem really high so it may be not worth it.
US PRs can enter Canada without a visa and Canadian PRs can enter the US without a visa. It takes about 3 hours to drive from Seattle to Vancouver, so you can visit each other on the weekends, etc.
You'll need to make sure you follow the rules and maintain your permanent residences in the US and Canada. You can do this at other points along the border too - I'm giving Seattle / Vancouver as an example because these are big cities with lots of jobs.
Definitely. After your wife gets her visa, you could try to follow-up with the embassy in July / August / Sept and ask them to try to expedite your background check.