What’s the difference between IPMI cycle and reset

This may not get you the text off the LCD, but have you tried the chassis and power subcommands? It's been a while since I had Dell equipment, but I believe one of these has power supply status information.

Alternatively you can install the OpenManage SNMP agent and query this information (and a lot more) via SNMP without having to parse ipmitool's output yourself.

I would take it down to single user mode, unmount any non-OS filesystems and remount any existing ones as readonly. Then run your firmware update tool and 'ipmitool chassis power cycle'.

It's not pretty or clever but should be safe enough