Выяснил - проблема в самом модеме. Консультанты Лайф об этом ни слуху ни духу.
Some Huawei USB modems have a mode called "HiLink" which provides for "driverless" installation on Windows, Macintosh and Linux computers. These modems usually have the HiLink logo marked on the outside, or have optional HiLink firmware that can be installed on the device.
The current Huawei HiLink modem firmware operates as a NAT router rather than as a traditional modem. HiLink provides no mechanism for the IP address assigned by the cellular operator to be "passed through" to the attached device, nor does HiLink provide any sort of port-forwarding capability.
For these reasons, HiLink mode cannot be used for remote access applications (e.g. Remote Desktop, VNC, web servers, etc.) where "inbound" connections are initiated by computers on the Internet. To use HiLink mode, your application must require only "outbound" initiated connections (e.g. web browsing, email, etc.), or you must implement a VPN connection to another device which is initiated by the router which has the HiLink mode modem installed.
http://www.proxicast.com/AbsoluteFM/afmmain.aspx?faqid=269
Пробовал перевести модем в т.н. режим "только модем" (метод), что по идее должно исправить этот случай, но так и не смог поставить драйвер.
Судя по всему, проще взять новый модем.