Here's what I would consider: -
In series with the microwave is a bridge rectifier capable of taking the microwave load current and AC voltage. On the DC side of the bridge is a power resistor in parallel with a low voltage relay such as 5V rating (or maybe even lower if you can get one). The power resistor is chosen so that when the microwave takes full load current, there is sufficient voltage across the relay coil so that it activates and turns the heater off.
When the microwave is done cooking, the voltage across the relay drops sufficiently and the relay drops-out and power is restored to the water heater. Here's a 3V relay made by Panasonic. It's got NO and NC contacts rated at 8A up to 250Vac. The order code (209-5597 ids for Farnell a UK electrical supplier so it's probably irrelevant in other parts of the world): -
The relay coil is 90 ohms and activates on (say) 2A taken by the microwave, the resistor and 90 ohm coil have to "drop" (say) 3V. This means coil and resistor together form a 1.5 ohm value. Clearly, as the relay is 90 ohms you can use a 1.5 ohm resistor. The thing to watch on this circuit is the microwave current. If it is (say) 2A max, then the resistor will dissipate about 6W and this is a little on the high side. Any more than 2A and I think I'd recommend a different technique using an opto-isolater built where the relay coil is shown. This could then activate a normal AC relay via fairly standard techniques.
Please let us know what the microwave current is when heating food and what is when just powering its clock - this is important to know for this design to work.
No need for phase angle modulation like on a dimmer for lighting, no need for PWM nor for switching on/off every second. It will introduce interference and the thermal capacity of the heater will be so large that you can easily switch on and off for full mains cycles and even every so many seconds (if your neighbors don't mind).
Switching at zero crossings is good practice, and a Solid State Relay can help you with that and is safe when properly connected.
No. 1000W heater operating cost will be the same, either way. However, a 240Vac heaters generally use less copper (smaller conductors for lower current), so theoretically you save few cents on the purchase price.