removing crafted mods

I have an item with the affix "can have up to 3 crafted mods" and two additional crafted mods, one of which I want to keep and the other one I no longer want.

To replace that one crafted mod, I need to bench-scour, right?
And doing so will remove all the crafted mods, including the "can have up to 3" one, right?
Then if I wanted to have the other crafted mod I want to keep plus a new crafted mod, I would need to add back the "can have up to 3" for 2 divine -- right?

Or is there an alternative way to replace that one crafted mod I no longer want?

The only alternative that comes to mind is using an Orb of Annulment. Depending on the item and affix u want to get rid of, an Eldritch Orb of Annulment might also work.

Obviously that can destroy ur item if it purges the non crafted affixes.

Otherwise u have to recraft multimod with 2 divines, yes.