You are correct. If you’ve been training above AeT, especially if it’s been over a long period of time, you’ll want to slow things down and train below AeT until your aerobic capacity (AeC) is restored. That may require changing your training plan.
Depending on how long you’ve been focusing on high-intensity training, restoring AeC could take a while, but it’ll be well worth it in the long run.
You wrote that your anaerobic base is strong. It sounds like it is *too* strong. Aerobic and anaerobic capacities exist in a relative balance with each other. As one becomes stronger, your lactate curve will move left or right accordingly unless the opposite capacity becomes proportionately stronger as well.
If you’ve been focusing on high intensity for a long time without also supporting or building an aerobic base, then your lactate curve has been likely pushed too far to the left for aerobic events.
The solution is to slow things down and focus on building aerobic capacity as described in TftNA. Rather than stick to a certain training plan or schedule, you may need to reprioritize.
I hope that helps.
P.S. Here’s a great illustration of how AeC and AnC work against each other: http://www.lactate.com/aerobic_anaerobic_animation.html. In the animation, you can adjust the relative strengths of each to see how a lactate curve will respond.