you could do a quick fade out/in and just say there was equipment failure in that section there.
That's a rather severe source issue there. Not much you can do on the error parts, but you do some left-right channel swapping to the extent that it's possible with the volume difference in left & right channels. Or just transcribe the words of the glitchy part, and edit it out, like page says.
I guess if you limited the living hell out of it, it would bring up the voice enough that it might be more audible. This is not music, you don't have to be dynamic. OK let me see what happens.
OK here's my test:
AppleAUPeakLimiter settings - attack time (shortest), release time (.005 sec), Pregain (I tried 33dB), and it made the voice sound good, except in the messed up parts which just sounded kinda muted.
It's bad, but not speaker-blowing. You could give it to the family as a bonus track??