Problem with monitors without DDC

I have a problem with the ATI Radeon 7000 Dual-head monitor detection in
Windows XP. There are two monitors and a projector, with one monitor and
the projector selected by a switch.
The switch's cable has the DDC pins missing, and one monitor (the older
one, something like an Acer 56e) shows up as "(Unknown Monitor)" on
another computer running Windows 98.

Here's the setup that currently works:

Primary -> Older monitor

/-> Newer monitor
Secondary -> switch +
\-> Projector

However, I'd really like to use the newer monitor as the primary, but when
I do, the ATI driver does not detect the secondary monitor, and so refuses
to allow it to be used. Note however that the BIOS puts the card into
clone mode at startup, and both monitors show in colour.

Is there some way to force it to use the secondary monitor even if it does
not identify itself? Or do I have to find some way of making the newer
monitor _not_ identify itself?

TIA.
Ben.