Top elite tier of AAdvantage program, Executive Platinum member - qualified when you fly 100,000 miles a year, or earn 100,000 Elite qualifying points, or 100 Elite qualifying segments.

EXP enjoys a lot of benefits that lower tier elites / general members dont, and rightfully so.

Unless you have the need to book the tickets the way you booked it (one direction from your account and the other direction from your wife's account), you can save the phone booking fee as it is charged per ticket. You can easily book r/t (or 2 one-ways, both direction) out of one account and save you $20 per each pair of tickets that are being booked separately from 2 accounts.

The $5 fee is not avoidable whether booked online or by agent.

The only avoidable fee is the phone booking fee if you can book this online. The question here is, how long the time has elapsed between your finding no availability online and calling AAdvantage to book. Did you check online again right before you call?

It is highly unlikely AA would release the hidden inventory reserved for EXP to general members, but it is a possibility.