Hi Erik,
Giving full accurate answers is difficult without photos, but going on your description..

Crown Guards:
It is not usual practice to grind these down, nor over polish them to an extent where they become misshapen.
Yes, we see many over polished, where the sharp edges are lost.

Cases:
The 844 case should be identical to a early 980.006 case.
I say 'early', as the later models, usually marked with an 'L' at the end of the model number - ie. 980.006L, these later cases were slimmer and housed a different quartz movement, and the bezel was recessed a touch into the case. A give-away is that they are marked with '1000' on the dial underneath the Heuer shield, along with an elaborate Heuer signed case back and a Heuer signed crown. (Like seen in the reply further down).

Markings:
Yes, some of the markings on the inside of the watches weren't high quality stamps/engravings.

Crown:
As touched on above, the crown should be unsigned. The later 'L' models have a signed crown, some even 'push in' and not screw-down.
Occasionally you see a signed screw down crown on an earlier model, and although technically incorrect, it's not a huge deal.. for the purists it should be unsigned, but I wouldn't mind one bit if I had a Heuer signed crown. There is also the high possibility that Heuer fitted these at service (in error), so although not 'catalogue correct', it is still 'Heuer correct', if that makes sense.

Book/Ref material
As far as I know, there is no Heuer diver book. You'll find a lot of information here on OTD, and on my blog - Heuerville. There is a lot of info on there as I started out collecting the Heuer divers.

Best of luck with your restoration - and if you need any other info, ask here, or email me, I'm happy to help.

Stewart
- Heuerville