In this part the relative clause that hinges on "some ethical problem" is extraposed.Do you have some ethical problem with what I’m doing that you can express in a unique way
=+Do you have [some ethical problem that you can express in a unique way] [with what I’m doing]?
which = some ethical problem that you can express in a unique way with what I’m doing = Xwhich might actually make me think that I’m wrong even though I’ll never admit it
Do you have X which...
There is no relative adverb in your sentence, only nominal relative pronouns.
Bit convoluted, is it not?
Student or Learner