I too have this issue and have went through each of your solutions as so....

Suggestion 1:  I was able to update the phone number successfully, but that only effects the number displayed on things like sales forms, it doesn't effect the number listed when attempting to verify changes made through out the rest of the platform thus making it impossible to receive a verification code.  In addition to the above steps you outlined, I also attempted to update the Business Owner mobile phone number under the Payments table of this same settings menu to no avail because it tries to send the verification code to the old number I just changed making it impossible for me to save the change.    

Suggestion 2:  Again following your instructions for updating the phone number associated with my Intuit account, I was able to successfully do so.  However, again, it doesn't effect the number listed when attempting to verify changes made throughout the rest of the platform thus making it impossible to receive a verification code.   I went even further choosing to turn on 2 Factor authentication as mentioned.  Ironically, when logging in, that code is correctly sent to my new number, yet all other codes are still being sent to my old contact phone number. 

Suggesting 3:  Following the link provided to update contact info on my QuickBooks Payments account.  I am unable to make any changes using those instructions, including the two phone numbers, deposit account etc, because again it still sends the verification code to the old number instead if the new one which I have now set two other places and is being used by two factor authentication but nowhere else apparently.   

I understand the need for verification in today's online environment, but this is really an overly complicated manner in which to implement a verification process and essentially makes it impossible for anyone who needs to switch mobile phone numbers to update theirs in your system.  They need to offer additional verification mechanisms besides solely a phone based call/text system because in the case of many small businesses when getting a new phone number you can't always retain access to the old number.      This process should take seconds, a minute at most, but instead I have wasted hours and hours trying to search the labyrinth of scattered setting menu locations hoping to figure this out just so I can make necessary account changes elsewhere.