If a creature you control has a mana ability with {T} in the cost, activating that ability to pay the activation cost of Heirloom Epic’s ability will result in the creature being tapped before you pay the ability’s costs. You won’t be able to tap it again rather than pay one of the mana in Heirloom Epic’s activation cost. Similarly, if you sacrifice a creature to activate a mana ability while activating Heirloom Epic’s ability, that creature won’t be on the battlefield when you pay the ability’s activation cost, so you won’t be able to tap that creature rather than pay one of the mana in the activation cost.