First, the wildlife photography is terrific! What camera and lens system are you using? This is ultra sharp, very good depth of field control, too!
As for the Dana 300, the gear teeth patterns would be okay if hard metal had not circulated through this unit. Note that the scraping evident at the teeth is uniform across the tooth faces, that's a good tooth contact pattern. The concern is the depth of this damage. These gears are typically 8620 or similar base metal with case hardening after machining. The depth of case can average 0.035", sometimes more, seldom less.
Given the case hardening, try to judge the depth of these striations from debris. With the heavier gear lube used in a Dana 300, you can likely get by without replacing all of the gears. We know that the intermediate gear is gone, especially if its inside wear at the needle rollers is contributing to the wobble and radial play. Any gear(s) that you reuse must have normal contact patterns.
If you want to minimize cost here, you need gears with teeth that will mesh properly when using a new or "good used" intermediate gear. If you seek out used gears, that's a gamble, because gears establish a wear pattern, and two used gears will increase the likelihood of tooth contact issues. So, if affordable, a new intermediate gear would be advised. You definitely need a new intermediate shaft, thrusts and the bearings.
Considering that this is a through-drive transfer case, in high range you simply need the input and output to lock up without play. The bearings and support for shafts need to be on tolerance. Make sure that parts will run in alignment. Be certain that the 2WD to 4WD synchronizing mechanism will work properly and that the transfer case shift positions will not jump out of gear. From photos, some of these parts look rough and worn. Check shifter detent parts carefully, these are small parts that play an important role.
As for low range, if you can eliminate the backlash of the gears, caused mostly by a loose intermediate gear, replacing some of the other parts is elective. You're not taking this Jeep over the Rubicon Trail with 35" tires and axle lockers. You simply want the transfer case gears to mesh properly, shafts to stay aligned, and bearing end plays to be correct.
Note: These last points are covered in my Jeep CJ Rebuilder's Manual: 1972-86. Proper end play shim adjustment at the bearing cap during final parts assembly is crucial. Bearing play determines parts alignment and bearing life, keeping the shafts spinning true with the correct bearing preloads.
Share what parts you think are reusable and how you're approaching the new parts needed...I'm here as a sounding board and extra set of eyes!