It is indeed likely to be a sendmail issue not a spamcop issue, hence the subject "sendmail woes".
[njh[at]bandsman ~]$ ping spam.spamcop.net
ping: unknown host spam.spamcop.net
[njh[at]bandsman ~]$
[root[at]bandsman log]# fgrep spam.spamcop.net maillog | tail -1
Jun 12 16:20:02 bandsman sendmail[15049]: m5CFK2t2015049: m5CFK2t3015049: DSN: <
submit.xxxxxxxxxxxxx[at]spam.spamcop.net>... Unrecognized host name spam.spamcop
.net.
[root[at]bandsman log]#