I did something similar awhile back. I ordered the 2nd subscription and after the first day it arrived I called the WSJ directly and asked them to merge the two subscriptions, effectively extending my primary subscription by 6 months. Only the first day's paper was wasted.
The only caveat is this wasn't with miles. I purchased my second subscription through a third party that was offering a discount, but I believe it should be the same scenario as your situation.