Greetings
Usually, you are allowed to bring one or two extra pairs on contacts (in the now famous plastic bag), but the rest must be packed in your checked luggage. So if you're going to be bringing 60 pairs of contacts, you'll need to check a bag. I think the idea of the regulation is to allow you to bring what you might need for the flight (i.e. a couple extras). I don't think you'd be able to justify 60 pairs as a prescription item as the prescription exemption is only for quantities of liquid meds needed during the flight (and in case of a day or two delay).
Wish I had dailies - I have two week ones and am allergic to most solutions (and not keen to test new solutions given the possible pain!) so can't risk not having a full supply of solutions unless I know for sure stores will carry OK brands at my destination. And very few companies seem to have solutions in quantities under 100mL.
Kate