Great post. Thanks. Some deep rabbit holes to go down but I will try to be brief.
A high level endurance athlete will have both a very high aerobic capacity along with a very high anaerobic capacity. This is difficult to achieve as the training of one tends to decrease the other. It can be done using a block style training program. It is a balancing act that should always err on the aerobic side.
However keep in mind that while there is no such thing as too much aerobic capacity there definitely is such a thing as too high of an anaerobic capacity relative to the aerobic side.
The longer the duration the event the less important is the anaerobic capacity. But anaerobic capacity is higher in stronger athletes. Strength supports power and power supports speed. So a weak athlete (who will always have a low Vlamax) will be slower than an athlete with the same aerobic capacity but a higher Vlamax.
This is where hill sprints come into the picture for virtually all mountain athletes. They are most specific power training you can do.
To your questions:
1) Increased pace at AeT is the #1 job for all endurance athletes. However if you are doing very long events (3 hours and more) then this is also your specific event speed. For shorter events under 2 hours then this is the base of support for the next step up the intensity ladder.
2) Increased maxVO2 should not be a goal. It should the effect of proper training. Please read my article The MaxVO2 Myth. Your focus should be on improving performance not improving a proxy for performance. While having a high MaxVO2 is a nice gift and many elite athletes have this characteristic. It actually correlates relatively poorly to performance. The article will explain in more detail why.
3) Increasing your pace at AnT the maximum sustainable pace/effort) should receive attention almost as much as #1 above once.
Recall from TftUA book that no one really has figured out the best way to do high intensity training. I am paraphrasing Aastrand here: Is it better to 4x4min of work at 95% of max VO2 or 1x16min at 85%? No one knows. This is why most coaches use intervals of varying lengths and intensity.
The advantages of Z4 intensity is that it combines ME, maxed out aerobic capacity (called aerobic power) and improves economy and will improve pace at AnT (high fractional O2 utilization). In other words, the whole ball of wax. It does all this but imposes a very high global load on the athlete.
Z3 does most of the above but with a much lower fatigue effect. It is not maxing our aerobic power usually unless maxVO2 is quite low.
For less experienced athlete we often use Z3 intervals as a way of introducing high intensity training. It can then provide a base of support for the Z4 that comes later. High level athletes frequently mix Z3 and Z4 workouts into a their training periods.
For high level athletes a highly polarized approach, the 90/10 mix of Z1 with Z4 (very little Z2 and Z3) during this period produces good results in improved pace at AnT (higher fractional utilization here).
Producing lower lactate at all intensities will come from ME and Z3-4 training. But more helpful can be working to improve the lactate shuttle and having a bigger aerobic base so that what lactate that is produced can be used as fuel by those ST fibers with their high aerobic capacity. This is an area I have had the most luck improving.
Another way to lower lactates at any pace is by improving economy. Do this with short high speed repetitions (what we call pickups or strides) and hill sprints. These will go a long way to helping this area.
If I have more thoughts on this stuff I will make another post.