Ok, if you can only receive (correctly) one /128 and you can ping correctly 2606:4700:4700::1111 from your router,
is meaning that the “cryptic box” probably is just configured to do bridging,
and the Juniper router of your ISP provide public IPv4 on DHCP and single IPv6…
So you must ask your ISP for further checks, in meantime or if your ISP can’t help,
you can use NATv6 with true IPv6 provided for free from hurricane electrics (see other posts) to use internally on your own network…
http://forum.mikrotik.com/t/my-isp-gives-me-only-64-ipv6-prefix-how-do-i-create-multiple-subnets/180205/5
EDIT: some edits for add link, detail on device used from the ISP, etc. …