Have you looked at booking through LH's website? I've seen cheaper prices, like a few hundred bucks. UA might also be an option.

If you're willing to do a connection, OW and Skyteam have good fares out of a *A hub. Not ideal with a baby, but something to consider.

Also if the "plan to collect to redeem" involves funding future FRA-YYZ trips, might as well forget it. As others have noted, you can collect AP points much more cheaply via other means (a credit card). AND the YQ on that route is insane because it involves AC and LH as only (nonstop) options. Since it doesn't sound like you're SE anymore...then no soup for you on waiving the YQ!