grammaticality - When "why would ..." becomes an embedded clause, should word order be changed?

Let's say I have the following "wh-question":

Why would a random person like me be able to see ghosts?

I want to turn this sentence into a complete answer statement. I would say:

I have no idea why a random person like me would be able to see ghosts.

To me, this sounds correct and natural. The verb would is moved from before the subject to after it.

My question is, is it grammatically incorrect to say the following?

I have no idea why would a random person like me be able to see ghosts.

As a native speaker from Canada and living in the USA, this sounds both unnatural and ungrammatical to me; however, I can't find any actual linguistic or grammatical references that say one way or the other.

Questions of similar structure I've examined (and come to the same conclusion) include:

• Why would a bag of chips be this expensive?
  
  
  
  
  • I don't know why a bag of chips would be this expensive.
  
  


• How would I open this door if I were Satan?
  
  
  
  
  
  • I don't know how I would open the door if I were Satan.
  
  


• Where would I find the bathroom?
  
  
  
  
  • I don't know where I would find the bathroom.
  
  

Forming those sentences using the wh-question word order seems incorrect and unnatural as well.

So, my question: Is it grammatical, and natural, to leave word order intact when turning a wh-question into an embedded clause?

NB: I have taken a look at this answered question as well as this unanswered one but neither of them address this particular scenario.