The discount applies for all passengers booked using miles from your account as long as all segments are DL operated. So even if you book a separate ticket for your wife but use miles from your account and you have a qualifying DL-branded AmEx, you will get the 15% discount.

You could also consider the Delta Platinum AmEx which is more expensive but comes with additional benefits that can offset the annual fee, including the companion certificate. Or you could consider a standard AmEx Plat and points can be transferred at 1:1 to DL for Skymiles but of course carries a steep annual fee.

Other options:
-Pay to transfer points at $0.01/mile. So transferring the 40K points you need would be $400 plus the $30 transaction fee. Whether that's worth it or not is a matter of debate but it is an option.
-Transfer hotel points or other rewards program points to DL miles. Usually not the best value but if you have any rewards program points that are otherwise sitting there that you are unlikely to use, at least you could get some value out of them
-Open a no-fee Delta Blue AmEx - you will get the "Pay With Miles" benefit and you could use "Pay With Miles" for your flights (on any ticket that is DL-marketed & DL-operated - not available on any itinerary that has partner-operated segments). Pay With Miles allows you to take $100 off the ticket price for each 10,000 miles on a cash ticket and you can apply across both tickets. So with the 160K miles you have in your account, you could take $1600 off the total purchase price.