RE: tool for starting/holding tiny screw heads?
For what it's worth, I had a similar screw holder on a flat blade screw driver. I haven't seen one in years though.
For a philips? Never seen anything similar. The best I have ever been able to come up with is a magnetic one...
Also, I found I have many different brands and sizes of screwdriver. One brand differs from another, sometimes enough that a philips bit will "hold" a screw, where another brand won't.
And finally, don't be afraid to throw a screwdriver away, once the bit gets rounded a little, the screwdriver is worse then useless, it's actually dangerous. I can't think of anything worse then when you're finishing assembly on a plane, the last thing is putting on the cowl, and the screwdriver slips off to tear or gouge the fuselage....