Is it permissible for me to stipulate at the time of the marriage contract that my divorce will not take place unless it is officially and legally documented, and is this condition valid in all madhhabs? And if it is not valid in the Hanafi madhhab, is it considered void given my adherence to this madhhab at the time of marriage?

It appears that this condition is invalid. If you divorce your wife, the divorce takes effect even if you do not register it, because it is not a suspension of divorce upon a condition. Rather, it is a precedence of the conditioned over the condition, so it is not valid. This condition does not affect the validity of the marriage according to the Hanafis and others, for marriage is not invalidated by corrupt conditions. Thus, the marriage is valid and the condition is nullified. Stating in the marriage contract that it is based on a specific madhhab (school of thought) does not obligate you to follow this madhhab in all matters.