I just used this same setup today except with the bishop. I also used Hawk cartridges, not T-Tech. The Bishop motor got really hot. I found that to push the hawk cartridges takes a lot more force than pushing the T-Tech cartridges, so I have to run the Bishop at higher volts. I needed 9 volts just to get the machine to start with the Hawk cartridges, whereas with T-Tech I only need about 7.5 Volts. I suspect this is why the machine was heating up so badly. And I have used the Bishop several times with normal tube/needle setup and it never got hot.

Don't know if the Vivace would also have this problem of getting hot, but if so I suggest using T-Tech instead of Hawk cartridges.