(maybe some obscure field to use in the header?)

You're on the right track with this one. Older spam software was notorious (?) for getting by with the bare minimum number of headers. Spam detection software used this, and scored messages on the absence of such headers.

I see you're injecting into the sendmail binary. I don't know how it behaves, as opposed to Postfix which will obligingly add missing Date and Message-ID headers. Be that as it may, your outgoing message should have both of those. If not, you'll have to add your own in your Perl program. Have a look at RFC-2822 for how to make sane values.

Some other standard headers that you could add are :

MIME-Version: 1.0
Content-Type: text/plain; charset=ISO-8859-1
Content-Transfer-Encoding: 7bit
[download]

(and make sure it really is 7 bit clean). Also adding Precedence: bulk or list might be a reasonably honest thing to do.