Connecting a Home IP Phone to a PBX

Question

Asterisk

Available:
1) Dedicated home without real IPv4;
2) IP phone that does not know how to Ipv6;
3) Office IP-PBX on Asterisk with a bunch of useful peers, but without an external IP;
4) Bonus - a friend has a router on dd-wrt with an external IP.
5) Admin rights on the PBX, phone, router.

The task is to connect a phone from home to an office PBX.
A trivial solution is to put the stub of Asterix on the router, register it in the PBX with another peer, connect from the phone to the router. Alas, with a torrent running there, you can forget about the normal quality of the voice.
Is there any non-trivial option to “make friends” between a phone and a PBX without external crutches? Providers at home and at work are different, getting an external IP address is unrealistic, paying money to third-party VoIP providers is a toad crushing.
Office Asterisk is hardwired, on AWS, version 1.2, it will not be possible to load additional modules such as skype connection to it.
Is the situation completely hopeless or is there a chance?

Answer 1

the dumbest option is to put a router that can do sane shaping, and give VoIP the maximum priority, torrents and other things - the minimum.

Answer 2

You can realize access from anywhere in the world via VATS