In reply to ChrisJD: of course the front would have to go a size bigger if its changeable. It may be the gap he needs before jumping on the Beinn.
I've just had a thought, it won't help you but it might help me and anyone else who cares to tinker. My son has a 16" Cnoc, I also have a Brompton which has a 16" wheel, I wonder whether I could convert the Islabike to a 3 speed bike!
In all honesty, I would be tempted to get a reasonably cheap second hand 'run around/hack' bike for the short time he needs to jump on the bigger bike. Also have a look at the Beinn because whith the seat dropped fully, and the stem dropped fully, the bike becomes pretty low down, albeit quite long.