Changing the codec is unlikely to help unless the bottleneck is at the central end. The problem you will get with a far end overload is that the VoIP packets will be queued behind higher volume traffic, like video of the Olympics or Zoom calls, and you would need to prioritise your traffic over the competing traffic, which is not something that is supported on the public internet, or insert large jitter buffers at the receiving end, which would result in unacceptable round trip delays.
Also note that the gains from moving from G.711 to G.729 are not as large as you might expect, because there are significant overheads on packet sizes.
Try IAX2 and the codec of your choice, although the GS softphone doesn’t support it many do, and always uses less bandwidth than SIP as it is binary not text baaed protocol and greatly reduced ‘header’ overhead.
What is relevant is he is apparently starved of bandwidth, if he doesn’t try it he won’t know the gain, IAX2 only ‘shares packets’ if you tell the connection ‘trunk=yes’ and then you will need a DAHDI ‘hardware timer’ available.
IAX2 is always more efficient than SIP , for a complete reference to better configure IAX2
You will see how to restrict codecs , set COS et al.
If using g729 over sip, setting the ptime to 60ms should get a theoretical 13.3kbps per channel .