Another thing to consider with any project is premature optimization and over-engineering. The use of phase-cutting for heat output control may, very likely, be overkill for a big vat of water and a ~300-watt heater (slow to change temp up, or down). A relay rated for 15 amps, running at most with 3, aught to have a very long lifetime, even at a relatively high rate of switching.

Either way, it'll be interesting to see how each approach compares. For the loser, to the next project the parts will go!