Well, part of what you are seeing is a consequence of the price of the
radio...it is less than half of the 7600 in my area. Since you are
experiencing the same problem but at a much lesser degree on the 7600
it tells me you live in an area saturated with strong signals. It
would take a more expensive radio to not be swamped by all that rf.

A simple way to reduce the problem might be to use the attenuator, or
just shorten the antenna when listening to shortwave.

A strong ssb signal can be controlled in much the same way.

The DE1103 is far from a perfect radio. The poorly designed memory,
somewhat buggy firmware and uneven backlighting make me think this was
rushed to production with little real world testing. Still, it is a
ball to just tune around in.