Upon reading closer it appears to me nothing needs be added to that list of three. Many is not all is my first observation of that excellent post. In my opinion there is ample scripture for believers to work through most of life's challenges. I like the phrase "Know your covenant terms." We have the instructions for most if not all possible human issues. If I already have the answer from the Bible, why pray for the answer? Should we not study the scriptures to show ourselves good disciples?
I say that to point out that our covenant (far stronger than any mere contract which normally has clauses by which it can be abolished) with God through Jesus is sealed in the blood of Jesus. The New Covenant is activated in us through our words of faith.
Above all those three "tools" ought to be invoked for the empowerment of our daily faith to walk the way of righteousness.
Upon encounter of things for which we have no suitable answer, answers obviously in the hands of God, we pray for guidance. But I believe most of our prayers ought to resemble the way Jesus taught to pray as in Matthew 6:
After this manner therefore pray ye: Our Father which art in heaven, Hallowed be thy name.  Thy kingdom come. Thy will be done in earth, as it is in heaven.  Give us this day our daily bread.  And forgive us our debts, as we forgive our debtors.  And lead us not into temptation, but deliver us from evil: For thine is the kingdom, and the power, and the glory, for ever. Amen.
That is a fine declaration of faith in the provision of God, the person praying meeting the conditions required for entry into the Father's presence. If as the OP states one is walking/working out his or her walk of faith then we have the assurance God will do those things daily because of His promises of His covenant toward us believers. God does it, for us, for the sake of His Son Jesus. God does it, not fellow believers. How God provides is an insignificant concern compared to the fact that He answers the believer's prayer to meet every need.
I am saying that if a believer stands on those three covenant principles, upon what God did through Jesus, then we ought not have to pray for necessities, we being more dear to Him than sparrows. We acknowledge in prayer what God already does daily, to His glory.
Prayer, such as that of Jesus in John 17, ought to be among believers primarily for seeking advancement of His kingdom on earth, praying to the Father in Jesus' name on behalf of others, chiefly fellow believers, and not focusing on ourselves.
In all that I will point out concerning your last statement that no believer in right standing with God ought to set his sights on help from neighbor believers. Rather, look to God alone who might channel blessing through our fellows. Perhaps God has in mind that the believer in need should go fishing, exemplified in Mt 17:24-27. When we look to our neighbors for help I as persuaded we limit God who can only be pleased by our faith.
Be blessed of God,
Be fishers of men.....DG