After logging in post reset, I lost various items due to death, including my lava bucket.
This meant that, as my island had been reset to almost nothing, I could not progress besides waiting for trees to grow for several hours.
Nonetheless, after a while I managed to organise a trade with a player who rarely frequents the Skyblock server, securing myself a second lava bucket, allowing me to harvest cobble once more.
However, I would like to be refunded my lava bucket, as the trade made could have been made with or without the circumstances involved, and the problem should not be necessarily considered resolved just because I found a way to obtain another.
TL;DR fell into void, would like lava bucket back, check death logs.