Eliminated AC...Now What Should I Do?

Without the heater control valve, your heater core will have hot water all the time.

There is no heater control valve on non A/C cars...they get hot water all the time, and the blend-door controls the amount of air allowed to pass through the heater core and into the cabin.
The A/C heater box has exactly the same blend door set-up as the non-A/C set-up. The heater control valve is just an extra measure to drop the overall temp inside the box assembly. You can pull it out and still have full temp control.