Update: I have improved this run to 3:51:28 - new video at    • Lufia II Speedrun (No Major Glitches/...  

Lufia II: Rise of the Sinistrals SNES version, played on North American SNES console (modded for component video output) with OEM controller (no turbo). Timing is from naming Maxim to breaking the final Doom Island Mystic Stone.

Nice overall improvement and almost a 4:4x skip.

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If you'd like to watch the run with live chat replay, check out the following recording:
https://www.twitch.tv/puwexil/v/1662450136