You want to log it as SIC but claim it to an examiner as PIC?

What does the regulation say? Read it?

Logging your experience as SIC while claiming it's actually PIC is ridiculous.

If you're going to claim it as PIC, then log it that way.

The notion of making multiple columns in the logbook to show "acting PIC" vs. "logging PIC" is also ridiculous.

You could wait until you'e qualified and assigned as PIC to begin logging PIC at your 135 operation. If you're in too big of a hurry and must absolutely run before you can walk, then log it as PIC while you're sole manipulator, go do your ATP, and race to the nearest regional in order to satiate that shiny jet syndrome.

Logging as SIC and telling an examiner that it's really PIC...no.