I don't think it is a matter of not having faith, we can simply do what we can to prepare to whatever extent is possible in a practical way. This is what proverbs indicates is practical wisdom and discreet to see a calamity and prepare , rather than just suffer the consequences. But to your point of faith in Jehovah's ability to provide, well what is there he cannot do? If he provided for Elijah by a raven bringing food , can he not have the birds of heaven provide in our time..really its not a question of will he or won't he....he can and will do according to his will. I know some at times feel this is like a cop out , but it is not. We have been told in Revelation 6 and Matthew 24 about the climate or happenings during this time and there was no guarantee to any servants of Jah of survival by miraculous help, famine, war, pestilences befall us all, this is the result of our (Adam and Eve's ) rebellion , we as a human race chose to leave Jehovah ....and now the consequences are here and very real....we have no guarantee of divine protection until the great tribulation and battle of Armageddon....the great crowd will be the survivors at that time, some of us may indeed die from and during the ride of the 4 horsemen , but our hope and trust is in Jehovah's Saving power by means of the resurrection.
Think of Revelation 6:9-12 Jesus brothers have to die to receive the reward and some will die as the others died , giving a witness....we have as Jesus said faith " that Jehovah is a God of the living and not the dead , as they are all living to him" as will we. Our test will be in as you said how do we conduct ourselves at that time , when our physical flesh is yearning , yes , desperate for the physical needs. Like our Lord and Master , we must subject our flesh to submission to our spiritual life and live. Jesus did not turn the stone to bread , his flesh most likely craved , yes demanded him to do so , otherwise , what kind of test would that have been? So our salvation , however Jehovah makes the way out, will be as you said a direct relation to our faith in his promise of the resurrection, and our spiritual life , not to food or any other physical means.
Just my thought on this anyway....love to hear back from you all.