I don't think it's doable. That guy's up to his neck in work year-round.
Literal
Impossible [quotative-と] think [feminine-わ]. Year-round, work [with-で] hand-full [possessive-の] person [because-だから].
手一杯 = 'hands full, overwhelmed' — 手 + 一杯 ('one cupful, full'). Casual expression for being swamped. だから gives the reason. The feminine わ and casual わ give this a specifically feminine spoken tone.