OK, thanks to Jeff pointing me in the right direction, I've managed to work this out.
For the benefit of anyone else who might need to make the mobile menu bigger, in iPhone-gantry.css, logo for this line:
body #rt-menu ul.menu li a {color: #aaa;font-size: 0.9em;line-height:2.2em !important;padding: 0 10px;text-shadow: 1px 1px 1px #fff;}
and replace with:
body #rt-menu ul.menu li a {color: #aaa;font-size: 1.2em;line-height:3.0em !important;padding: 0 10px;text-shadow: 1px 1px 1px #fff;}
These settings worked for me using Modulus, but YMMV on other Gantry templates.
To make things even easier to navigate, I will just use a single top level menu item "MENU" and branch all other menu items off of this.