Hi Chris, sound like exactly what happened to me.
Got some new relays on their way thanks to ayjay and they are 30A so a little over-spec for what I need which is nice. I have looked at the wiring and brushed up on my electronics. I have decided there is no problem with it. Maybe I am wrong but the whole electronic side of it is quite simple. It just looked very complicated to start with!
I had many a successful firing with the old relay before it broke but I am now replacing both of them. Mine is also an old kiln that looses heat fast but I never thought about it causing more damage to the elements, good point.
Maybe it is time to order that ceramic fiber to fill in some gaps