I've got it to almost work.  I've used screen as follows :

in ~/.screenrc on a machine here that I have console access to.
screen -T scoansi

and then started screen, and gone through a couple of jumps to
get to the SCO box. I'm testing on my NetBSD server here, not the one
at the client site.

$term propagates through to the first hop just fine (ssh to a NetBSD
bastion) and then I telnet -8 from the bastion to the SCO box.  The
screen now doesn't fill with control chars and mystery noise and it
displays pages properly, colours look right, the text entry boxes are
in the right places and empty, but it's not (seeming to) deal with
function keys.

The app uses F4 to go back a page, and F4 doesn't respond.  Is that
maybe a behaviour of NetBSD (or ssh?)  It does work fine with the same
basic setup but coming from a win32 ssh client (PuTTY) via the same
NetBSD bastion so I don't think the problem now is at the SCO end as
such.