Could we set the timer to start on map "sp_a1_pr_map_002", and/or "Time Travel" from the chapter select seeing as the first map is just a cutscene, similar to Portal 2's starting cutscene.

I view the opening cutscene as the bedroom portion of Portal 2 intro cutscene, which isn't timed since you can't speed it up. The next map is where you first need to solve a test and therefore is the first time the run can be affected. It's also the first place the crosshair appears. I think we should also follow in Portal 2's footsteps by adding the cutscene time to our timers. (Intro cutscene is 6402 ticks or 1 minute 46.700 seconds )

think it should start as soon as the crosshair starts being shown

This is listed in the game rules.