Door hangers on double arched doors.

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arched double doors

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Solid or is there some glass?
Balsam Hill makes a magnetic wreath hanger than I’m sure is outrageously priced and could be found cheaper elsewhere.
If glass, you also have the option to suction cup it (there are tons of options on Amazon here)
A large nail can be done right and not look obtrusive
You can also use a large ribbon that is anchored on the inside of the door, hangs over (like your over the door hangers that you’re avoiding…though maybe you could find one that’s malleable and bend the crud out of it?).
To mount it inside, you may be able to use a little tape, use a flathead tack at the top of the door, or, if these doors are not used very much, you may be able to get away with a small anchor like resistance bands use (basically just a plastic “catch” that won’t slip through the door, but it’s useless if the door is opened). In trying to find the proper word for “over door anchor” to search, I came across this which may actually fit your needs if you like the “hang on ribbon” approach and are able to cleverly use some sort of bow/material that hides the link.

Been here before. Just get some waxed thread (amazon or army surplus store) ,it’s super tough and can hold a ton of weight. Tie a slip knot around a flush thumb tack and pin it in the center of the curved top rail (top of the door.) this way your door can close and also the cord is thin enough where you won’t really notice it. Cut to length after and hang wreath or decoration. If your doors are tall, you might need some double sided tape to keep decoration from moving around on the operable door. Good luck.

Check out the Command hanger strips at Home Depot. I believe 3M also makes a similar style.

They use a removable adhesive strip and can hold plenty of weight with no holes.

I use these for Christmas wreaths and other door decorations