Only official instrument approaches authorised under FAR?

In article ,
Peter wrote:

FAR 91.175 (a) suggests that it is not permitted to carry out a
descent in IMC except on an official published IAP.

It does more than suggest, it states it quite explicitly (for most of us,
neither of the exceptions are likely to apply):

"Unless otherwise authorized by the Administrator, when an instrument
letdown to a civil airport is necessary, each person operating an
aircraft, except a military aircraft of the United States, shall use a
standard instrument approach procedure prescribed for the airport in part
97 of this chapter."

How would it differ if the entire procedure was done in Class G?

Not in the least. All IFR rules apply in class G except for the
requirement to obtain a clearance.