The command /execute as @e[type=minecraft:item_frame,sort=nearest,limit=1] run data merge entity @s {Fixed:1b} will make the nearest item frame to you unbreakable to players in adventure mode. Alternatively, /execute as @e[type=minecraft:item_frame] run data merge entity @s {Fixed:1b} will make all item frames on the map unbreakable.

These only really work if there's an item inside of the item frame.

Well using a commend is not a hack; but serious - that changinf my way to build in Minecraft very much; that is the biggest thing to me since I found the possibilities of heads.

PS: I am using a very similar designe for a writing table as you prestened here; but instead of flower pot I am using a ink bottle head (maybe you should take a look at my head collection) which improves this even a bit more ;)