Constant Offset Floating Supply
At the 1A level you’re almost certainly going to want a 10W switching supply, however 12-200V is a very wide range to use that for a power source. 

A negative linear regulator would dissipate almost 200W with a 200V supply so that would be very inefficient. 

If you have another supply such as 120VAC you could likely hang an isolated AC-DC supply or an isolated DC-DC converter output off the positive rail of the variable supply. 

This is not an uncommon arrangement for something like a inverter TIG welder output stage.