I’m assuming soup is Lach (moist ,obviously!). Can you have reheated soup for Shabbat lunch if you leave it next to the Blech and not directly on it? If not - any suggestions please. Just moved to Really cold climate and soup would be great.

Both the Shulchan Aruch and the Rma agree that there is a concept of "Bishul Achar Bishul" (it is forbidden to recook something previously cooked) regarding things that are Lach. Hence, you are not allowed to reheat the soup if it has been off the Blech when Shabbat started. If you would like to have the soup you should leave it on the Blech, or serve cold. Rabbi Ro'i Margalit