If bubs is still high it could be a positional problem too and not that his head is too big. Often babies that aren't in the best position for birth don't engage or don't engage fully. It could be that your baby wont engage until labour starts. You could try some optimal positioning techniques from the spinning babies website www.spinningbabies.com to see if that makes a difference.

failing that it is possible to vaginally birth a baby with a large head (I'd like to know what consititutes a 'large head' - is it 35cm, 37 or even 40cm?) Babies skulls are designed to be birthed vaginally and the plates of the skull will mould themselves to fit through the pelvis and birth canal (don't you just love that term LOL) - hence why some babies look a little worse for wear.

ETA - if baby is still high on the 5th, would you be happy to wait another day or so and have monitoring or an u/s to check placental function to avoid a c/s? That is another option you have available to you

Good luck and I hope that the wee one decides to come soon for you.