As you correctly identified, this is what many collectors refer to as a sei tacche. Yours is from around 1946, as per the 7-digit serial number on the movement. The "LXW" marking on the balance cock suggests that the watch was originally sold in the USA. All three hands are the correct style. Unfortunately, the dial has been refinished at some point. This hurts the overall value of the watch significantly. As you noted, the crown has been replaced with one from a Mido. The "1906" is an individual case number and the "23,044" is an order number. If you contact Longines with photos and the serial number, they should be able to provide you with the reference number, along with the original date of invoice and some other information. The missing case screws are common
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