Health: Your distinction is irrelevant. The Cheftza of the coil is unchanged, regardless of whether they are always or only sometimes covered. The coil remains the same coil.
Anyways, that answer was all l’Shitascha. As others have pointed out, your understanding of Dumia l’Meleches HaMishkan is critically flawed. Sewing with a machine is still Tofer as is harvesting with a combine Kotzer, or for that matter uprooting by hand. As the Eglei Tal and Shvisas HaShabbos explain, when the outcome is identical to the Ma’aseh haMishkan and only the procedure is changed, it becomes a Toldah. Still d’Oraisa, just not the Av Melacha. So, if you wish to claim that a crockpot is only a Toldah of Bishul, as Tzli and Tigun are, and not the Av, there would be what to discuss, however there is no practical Nafka Mina. However, it is rediculous to claim it is only d’Rabbanan.