Audition's multiband compressor (from iZytope) is fairly useful with this.  I forgot it was even part of Audition.  They also seem to have a declipper now as well.  Applying the internet delivery preset and soloing the middle two bands seemed to help understandably on this audio.  I haven't really played with multiband compressors much, seems like it may be very useful at helping some types of bad speech be more understandable.  mettelus recipe's result is much better than anything I came up with inside or outside Audition though.

That multiband is nice, but not a one size fits all and can easily generate artifacts. It is the best built-in next step for the plosives and evening the track segments.

iZotope apparently makes some plugins integrate with AA (as menu items). I hit one effect to see what it was and it popped off Neutron and ran an automated routine with no insight as to what it was doing... Just said "Processing Neutron" and done. After I saw that I began wondering if that multiband is a stock AA plugin or from an iZotope plugin I purchased.

Thank you mettelus and everybody else for all your help and detailed instructions. It was very informative and it helped a lot.
 
mettelus please pull the file down from dropbox because I have already transferred it to my account. Thank you.

Done.
 
Not sure if you are familiar with the use of compressors. Jeff Evans posted an excellent "How to" a while back that you may find useful as you move forward with things. Due to the variations of that track, working with segments that are similar is the best way to attack it.
 
AA's "Auto Heal" tool is something that is useful for rogue transients, and I have found most useful using the sonogram/spectral view. If you span a transient, so that the tool can see "good info" on either side (using the select tool to create a box), it has the best chances of performing well.