Using this command to move an existing painting vertically

/data modify entity @e[type=minecraft:painting,sort=nearest,limit=1] TileY set value 18

The painting still exists in the world but doesn't show up anymore and is no longer able to be interacted with although it still prevents other paintings from overlapping and still pops off the wall if any of the blocks behind its new position are destroyed. If the player quits and reloads then the painting shows up correctly in its new position

Additionally, using the following command to change the appearance of an existing painting visually changes nothing until quit/reload

/data modify entity @e[type=minecraft:painting,sort=nearest,limit=1] Motive set value "minecraft:pigscene"