You can send your adjustment application with an advance parole application (which is free). That case you are covered with a valid H-1B (dual intent) visa and a parole document.
Whether to send the documents before or after your trip is a decision only you can make.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature and does not constitute legal advice, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship. Answers on Avvo can only be general ones, as specific answers would require knowledge of all the facts. As such, they may or may not apply to the question.