I have derived a solution which employs a \Needs command in a custom tex4ht .cfg file to support automatic conversion from included PDF files to PNG. However, two runs of mk4ht are required to produce a valid document, because the .odt file is compressed just before the command I specified in the \Needs directive is run.

When looking at the .lg file, the "File:" directives appear just before the "--- needs ---" directives.

Is this intended behavior?

Minimal example: https://github.com/muelleki/lm-template/tree/oolatex-needs

See the last line of the Makefile for the compilation command