It does not work in your 2nd or 3rd sentences because of other grammar problems: I couldn't go to see my doctor due to / because of my afternoon shift work. My sister doesn't want to pay my bill because the responsibility for my money is mine. The sound doesn't come out of the speaker due to / because of a towel that is covering it.
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Mister Micawber...a towel that is covering it.I'm curious why is this changed? not "a towel to cover"?