Arrive in Tokyo 27 Dec, too late to reserve trains to Shikoku for 28 or 29 Dec + back to Tokyo on 3 Jan?

Hi there,

I am thinking of getting JR Passes for a family visit to Japan at the end of the year, mainly to travel between Tokyo and Matsuyama (flights arriving Tokyo around 27 December, leaving Tokyo around 4 January).

Is it likely to be too busy to get reservations on trains when we activate the Passes on 27 December? e.g. to travel on bullet train to Kyoto or to Okayama on 28 Dec, and then on to Matsuyama on 29 Dec or 30 Dec?

I'm also concerned that the reserved seats might already be fully booked by the time we activate the Rail Passes on 27 Dec to be able to reserve train seats on 3 January to travel back Matsuyama to Tokyo.

Is there any way to avoid uncertainty, e.g. reserve seats after purchasing the JR Pass but before activating it?

We will travel with a small baby, so if possible I want to avoid queuing for hours on station platforms...

Would be very grateful for any advice you may have, thank you!

Harri