llckll, plan where you want your splice box before you go to HD.They sell most cables by the foot although for 12/2 you can by smaller rolls than 50 feet.Hopefully you dont have to go back to the panel.And do pick up a test meter.
It would be very helpful in helping your figure out this situation if you could tell us whether the power from your panel to this outlet box comes from underneath, or if it comes through the wall. That would provide a starting point as to how to move the electrical box from the baseboard.
An electrical meter as was suggested by someone else can be had for ~$10 and would help determine where the source of the power is coming from.
Another question is have you determined which breaker controls this circuit and what else is on this circuit?
Figuring out some of this information will help people solve this situation with you.
Just to give You some other ideas,if it is possable,can You attach some round duct to the present one,extend it into the room and put in Floor registers. This would clean up the wall nicely. If this would help then you could cut about a foot of the wall out to gain access for any wiring.Then You could finish with new base.