Have a custom escutecheon fabricated and installed.

Really moving the escutcheon back will be easiest (I didn’t say easy). Coat with paint stripper and cover with plastic for 24hrs. Remove plastic and scrub off paint with a wire brush. Repeat until the escutcheon and that small section of pipe are clean. Then gently move the escutcheon against the wall. It will take some time and curse words but almost no cost if you are a little handy.

What Hallett said. To add: Look to see if there is a set screw/ Allen type screw. If there is one, it will probably be on the underneath side of the escutcheon. Besides paint removal, multiple applications of penetrating oil over the day/ days/ week to loosen the rust grip. Be patient and give plenty of time for the oil to work. Keep reapplying the penetrant every time you think about it.

The top escutcheon in the first photo looks like it has been tack welded. If so, you will need a grinder to remove the weld.

Work carefully and be gentle. Cast iron (the escutcheons) is brittle. i.e, don't go beating on them with a hammer.

Thank you all! Very helpful