Again, the point is being missed and a lot of irrelevant information is being posted, by people with the best of intentions.
Please read the relay data sheet, before posting anything about arcing, inductance etc. The relay is specified to switch slightly inductive load, cos?=0.4, at a reduced current and voltage. Even if the heating element is slightly inductive and the circuit is under-damped, it will not be that inductive. A quality relay, specified to switch a 25A resistive load at 250VAC, will be able to withstand the arcing created by a very slightly inductive 13A heating element. Another thing to note is that it's a water heater, so the inrush current will be negligible, because the resistance of heating element wire doesn't change that much, between 5
oC and 100
oC.
http://www.sanyourelay.ca/public/products/pdf/sfk.pdfI repeat, arcing, inrush current and inductance are all irrelevant here and discussing them will not help. The solution is to buy a decent relay.
240V double pole contactors are about $15 at a local HVAC parts store. Or get two single pole contactors plus a high current rectifier diode to bypass one in order to allow selection of full or half power.
Yes, that's a much more sensible solution, even if it's a little overkill, you can be sure it'll be reliable. Be careful about half wave rectification of large loads though, as an upstream transformer won't be happy, although I suppose 3kW isn't big for a distribution transformer.