The yellow line is designed for aircraft LEAVING the runway.
Certification flight testing assumes that the full runway length is used, within the constraints of the individual aircraft's geometry and ground manoeuvering capability. The same tests assume full thrust before brakes release. A great number of FAR 25 certified aircraft assume that the rear-most portion of the undercarriage is JUST inside the runway end (even if you needed a tug to push you back there).
Several FAR 25 aircraft that I've done certification work for operators compliant with JAR-OPS requirements have to make allowance for line-up from the manufacturer supplied AFM data. JAR-OPS supplies a good formula for this, which is usually acceptable to such authorities.
To respond to the original post, my recommendation is -
(1) Leave the yellow line at the runway holding point, manoeuvre so that the outboard gear is just inside the taxiway / runway end, and line up without any wasteage of runway.
(2) If your runway alignment is not quite perfect, don't waste any valuable runway tidying it up, correct the small centre-line / alignment error in the first 200 to 300 metres of the takeoff roll. Whatever amount of runway that you waste here is the distance that you'll overrun the other end of the runway in a performance limited rejected takeoff.
(3) Apply full thrust on the brakes before brakes release.
(4) If your actual Takeoff weight is below maximum, by all means conduct a rolling or roll-on takeoff (which includes gradual application of thrust), provided that correct allowance for rolling / roll-on start is made in accordance with the Flight Manual, or your Company Operations Manual.
If you take a look at the 2 major sets of certification rules, FAR 25 and JAR-OPS, you will see quite generous 'buffers' for the continued takeoff case, but very very little for the rejected takeoff. Accident statistics prove this time and time again.
The Runway behind you, the sky above you, and the fuel that you didn't take are without doubt the 3 most useless things in aviation.