How can I permanently write on HDPE plastic?
From experience, one good way to permanently mark on HDPE is a paint marker. The following is just the first one I found online; no endorsement intended:

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&nbsp;&nbsp;&nbsp;Promotional image from uline.com

They tend to be stinky and a tad messy, but they usually leave clean, visible lines and are basically indelible, requiring a lot of scrubbing with alcohol, acetone, etc. to remove. No idea how well it'll survive power washing, though.