After some more experimentation, the problem was not with the shell at all, but with the implementation of Telnet on Busybox. On my version of BusyBox (1.00rc2), piping anything to Telnet didn't work.
echo blah | telnet -yrDumb
Should have at least made telnet complain about usage. It didn't. I grabbed the most recent version of inetutils (1.9.1) and compiled its telnet for the TS-7260. It works like a dream (read: it works) now, and is consistent with the behavior I see using telnet and bash on my normal linux box.
Thanks for the help!