I recently bought an 844/3 on eBay and have started the process of getting it in proper, reliable shape.
I'm dealing with a local vintage dealer, who has several of what I consider to be very experienced watchmakers on staff.
Although he used to deal in Heuers quite extensively, we're a bit stumped.
I am a novice, and greatly appreciate any help with the following questions.
Unfortunately, I don't have the facility to include photos, plus the watch is currently with the dealer.

In the various catalogs, the crown guards look to vary quite a bit from watch model to watch model, especially as regards the mid and small size cases.
But the 844/3 case appears to have been polished (even ground down) quite a bit around the crown.
Is this a usual practice, assuming a lot of wear in its earlier life?
Or did the 844/3 cases differ from say the typical 980.006?
I certainly understand and mourn the value lost when some hack carelessly tries to make the watch "look better".

The auto movement appears correct, except the "Heuer" on a cover plate looks to be rather crude.
I've seen photos of the same movement (ETA 2872 I believe) with the same crude marking.
Is this marking typical - seems rather unHeuerlike?
If real, I will proceed with an overhaul (not keeping good time).
If not, I will probably replace with an unsigned swiss made version ($100) until (if ever) the correct one comes along.

It currently has a TAG crown (seems a common replacement) that will get replaced.
Were "Heuer" signed crowns ever used on the divers? I also have an 980.006 with an unsigned crown.
I found an NOS signed crown ($140), but only want to use it where appropriate.

Finally, does there exist a source book that includes an in-depth review of the divers?
I have "Mastering Time", which barely mentions the divers.
I've ordered and am awaiting delivery of the Foulkes book, but hold little hope.

Thanks again for whatever assistance you may be able to provide.