I've made some progress with this, but I may also have hit a brick wall. I configured DSLstats to use SSH as an option, and in SSH mode it logs in once and stays logged in until the user hits the stop button or closes DSLstats down. This worked quite well on my Linux system, and it collected data once a minute for about 40 minutes. At the same time another instance of DSLstats on a different machine was connecting by telnet and uploading to MDWS.
However, after about 40 minutes the modem abruptly rebooted and the telnet session resumed but the SSH session didn't. I got the impression that the SSH session was stressing the modem too much. Data collection by SSH was very slow - after the initial 6 seconds to log in, each sample took about 12 seconds to collect the full set of data.
I'm not sure where I'm going to go from here.