Do ISPs really give out /128s? That's, erm, that's monstruous! Mine gives a /60 but their router doesn't have any way to use it, which is a bit shit. Still, 10 gigs symmetric...
You absolutely can get a certificate for an IP address. Clients should verify them based on the common name, and a subject alternative name has various field types including IP address.
A quick Google search shows various certificate authorities who will issue certificates for IP addresses.