This route might be able to go down to 18:XX with perfect RNG and execution but this was the fastest I got it in a dozen runs.

A better route might involve a change in class (unlikely, Jazz Agent is great), or adding combat to the run for the stat boosts & two fights in Day 4 — the nemesis to avoid the stat penalty, and the ziggurat laser trap to skip its long cutscene. Or one could find a skip for the cutscene instead; you get sorta close by exiting to main menu while mid-cutscene but alas! While that makes it look funny it, unlike the Transformer skip, doesn't actually save time.