Backlash doesn't usually show up at the driveshaft (noticeably,) since it's a small amount. D44 ring gear backlash spec is .005"-.010", but you'll need a dial indicator and a magnetic base to read it properly (and remove the cover, and jack the rearend up so the wheels and axle are free.)
You'll feel a "little" play in the pinion when you try to rotate it, but it's not going to give you an accurate measurement. As long as the pinion shaft doesn't wobble about, you're fine there (a wobbling pinion means that the pinion shaft bearings are hooped.)
You'll also feel some play at the transfer case end - both endplay (it's a slip yoke, unless you've put in an SYE) and sideplay (there's some small clearance between inside and outside splines, and between the slip yoke and the support bushing.) I don't know how much, offhand, of each - but the endplay will certainly be plenty (the slip yoke usually sits - static - in the middle of a couple inches' worth of travel.)
However, there's no proper way to measure "healthy" play at the driveshaft, so drop that idea.
The "thunk" from R to D is fairly normal as well - you're reversing drive direction in the geartrain, and that's going to take up all of the freeplay in one direction (that's built up as it all gets driven.) Pretty much any vehicle will do that - because gears require some small amount of freeplay ("lash") to operate and remain lubricated!
Things I'd check?
- Driveline Cardan joints - particularly in the rear driveshaft. Test by gripping the driveline with one hand to either side of the Cardan knuckle (so the joint is between your hands) and twist in opposite directions. There should be no noticeable play (if there's .001" or .002", you won't notice it...) when you twist back and forth. Test each joint individually (you can hold the pinion yoke in one hand and the shaft in the other, then hold the shaft in one hand and the slip yoke in the other.)
A similar test can be done on the front driveshaft, and you can check the Cardan joints behind the front wheels in the same manner (just with a bit of creativity. I cut and sanded down a bit of 2x4 to fit snugly in the front wheel yokes, and can hold one side of the knuckle with that and turn the hub with the other hand.) Yes, check the fronts as well - since any freeplay there in the Cardan joints can be noticeable as noise.
- Check for excessive stretch in the transfer case chain - you should be able to turn the front output yoke a couple of degrees or so in either direction due to the natural slack in the chain - but if it's more, think about exploratory surgery.
- Checking the clearance of the side gears to the differential carrier might prove instructive - excess clearance there can mean excess clearance between the side gear teeth and spider gear teeth, and that can be a problem. Specs below (from AMC FSM - but they got their info from Dana, and it hasn't changed in 30 or 40 years...)
DANA 30 FRONT AXLE:
.000"-.006" - Side Gear to Case Clearance (measure with feeler gage, prise gear away from case side)
.005"-.009" - Pinion Gear to Ring Gear Backlash (measure with dial indicator on ring gear tooth, keep measuring tip as close to straight in line with the measurement as possible. Dial indicator is mounted on magnetic base - which makes it nice and rigid, if you did your setup right.)
DANA 44 REAR AXLE:
.000"-.006" - Side Gear to Case Clearance (measure as above)
.005"-.010" - Pinion Gear to Ring Gear Backlash (measure as above.)
I don't have any specs handy on what you should find in the NP231 or NP242 transfer case chains - I say go with intuition on that one.
Of course, this has had me making a few assumptions - even if you've got vehicle information in your profile, please put it in the post when you've got a problem like this! Some of us are all over - and going back and forth to profiles hoping to find essential information (year, make, model, powertrain, mods, ...) isn't what we normally think of...
