I'm wondering if the constant 5% discharge/recharge cycle ASUS programmed into this laptop contributes to the bulging battery.
Nope. Constant charging at 100% will reduce the useful life of the battery faster while periodic cycling between low but not empty (like 20%) and high but not full (like 80%) would maintain the longest life. Allowing the battery to discharge slightly and then topping it up is a compromise to extend the life while ensuring the user has an approximately full charge whenever they might unplug and go. There's nothing about that which would cause a catastrophic failure.
Deep discharge such as draining the battery fully and then letting it sit for months can cause damage, rapidly dis/charging, or attempting to charge an already full battery can all cause damage. The internal BMS should sever the connection to cells before they get out of bounds. It's likely either the BMS failed or there is a physical flaw in your battery pack, like the internal short in the Galaxy Note phones.