Early sixties race cars front badge without outer rim?

Some early sixties Ferrari race cars (namely the Fantuzzi SP's) had a rectangular recess for the front badge. Two bolt holes. However, I have just confirmed that a late 50's OMEA badge is too large for the recess. The badge sits on top of the recess, completely covering it. Here is a picture of the kind of badge I have:

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If I look at pictures of the early '60s race cars -originality of the bodywork today is another discussion but I could not find clear enough period photos- it is clear that their badge sits in the recess.

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https://www.carrozzieri-italiani.com/wp-content/uploads/2019/07/0c2cb79e96c044b168c8ed73d5dc8289ba831d19-1200x750.jpg

If anyone has access to a (good photo of a) relevant car with recessed badge (not all had a recessed badge, eg 250 GTO has a regular badge above the surface), preferably Fantuzzi, could you confirm what their badge looks like?

Is anyone aware of badges with smaller dimensions than the 34.90mm x 59.80mm of my OMEA badge? Or badges that came without the outer rim maybe?

Or would they simply have milled the outer rim off a standard badge for the race cars?

By the way, pictures of the Ferrari webshop SP nose (*replica*, which they fail to mention...) are useless as that replica contains multiple deviations compared to the original cars. Among which, a non-recessed badge.

By the way 2, I have seen pictures of later Ferrari badges in a rectangular recess that had the full outer rim, so either those cars have a larger recess or indeed there does exist a badge with smaller dimensions.

 

The badge I showed above is described as 60s-70s, mine was described as late 50s but looks identical, in general I can't tell 50's vs 60's badges apart anyway.

But the point remains that those badges are too large to fit the car, so either Ferrari/Fantuzzi modified the badge or a smaller version exists.

 

Only now do I see a closeup photo online.

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https://static1.topspeedimages.com/wordpress/wp-content/uploads/jpg/201908/1962-ferrari-196-sp--2-3.jpg?q=50&fit=crop&w=500&dpr=1.5

So as I suspected, no outer chrome edge on the badge.

Would this kind of badge be available somewhere? Or would I have to mill down a regular vintage OMEA badge.