Just a quick update in case others find this thread in the future.
At the lower sync speeds, the network stability issues continued. In desperation, I switched the modem to bridged mode, using an external PPPoE client to connect with the ISP. This was stable! It's been up all evening and overnight with no drops and everyone in the house is happy again.
Perhaps the HG612 can't cope with something in my network when the HG612 does PPP or NAT which results in DSL losing sync. It's hard to know as the syslog doesn't say much, even when configured at debug loglevel.