Crown for a JLC E393

Hi all. I have a 18k Jaeger-LeCoultre E393 with a cal. K881. It has a generic replacement crown which I'd much prefer to replace with an original one. I don't know the exact dimensions for it, but using this listing of a near NOS example as a base and some pixel counting, I came up with the following dimensions: 4.5mm in width and 2.2mm in depth/height, which of course are approximate but should be close.

The crown from the front in that listing:


From the side:



I'd really appreciate if someone can give some pointers to the exact dimensions of the crown and hopefully, where can I source one. I've been looking on eBay, but not been that successful.

Bump in case someone that may help missed the post.