So I'm a bit confused about how we are supposed to sign up for shore
excursions without knowing the cost up front, and I'd appreciate some
suggestions from anyone who has gone on a Princess shore excursion at any
of these islands previously. Thanks!

Have you set up your own account on the Princess website? I believe that,
once you set it up and then login, prices will appear, as will the ability
to purchase the excursion of your choice.

You need all of the usual stuff to register...and then you will need your
booking code for your cruise. You should have all of that by now if your
cruise is a week away.

Note: Princess will not charge for the excursion until you are onboard, you
will, basically, make a reservation for an excursion. There should be a set
of rules about charges, etc on the website.