Ratings on solid state relays are even more confusing. The current rating on an SSR is what it will handle when the relay is artificially held at 25C. This has very little bearing on the temps it will see in your actual circuit, and the actual temp of the device if you were to try to pass the rated current is almost universally going to eventually reach much higher. This is one reason why people say to always "derate" an SSR by 30% or 50% or whatever. It's because they don't get into the details of the datasheet and just read the current rating... then they decide the part is "inferior" or "falsely advertised." Actually, around here, the most common conclusion is that the relay is "cheap chinese crap." But this is in fact how all transistors are rated.
For something that isn't going to turn on/off but a few times a day, I think the mechanical relay is better, anyway.
As others have mentioned, at really high current levels, you start getting into contactor territory. But for what you are asking, a mechanical relay is probably the best thing for you, anyway, so you don't have to learn about these other things, yet.