Each element will be pulling 1500W/120V = 12.5 amps. Standard household wiring handles 15-20 amps, depending on the wiring, so you need two separate circuits. You'd need to find two outlets in your house that run off of different circuit breakers, (not too tough). Then you run a cord from each one into your control box.
You will need a second SSR like I linked above, but still only one PID and RTD probe. The two SSRs will be wired to the PID control in parallel. One power source will go into "SSR 1", one power source into "SSR 2". The PID can be run off of either (not both) power sources. Each SSR will then control each 1500 watt element, but because they will be run off of the same PID, they will both switch on and off at the same time.
The rest of your math was right, except you assumed that your heat loss to atmosphere would double when you doubled the elements. In reality, it would stay the same, so you'd have (2 * 1500) - 200 = 2800 watts of effective heating power, not 2600 watts.