If you filled the differential until oil ran out the fill plug, you have the correct amount of oil. Sounds like the axle seal is bad. It's been awhile, but you have to pull the axles, and I'm pretty sure the carrier to access the seals on a D30.
You are correct, sir.
-Remove diff cover and pull axles
-Remove retainer bolts (be sure to mark L/R and top/bottom on retainers, they have to go back on the same way)
-Pry out carrier...shouldn't take too much effort, but a little help with a pry bar will probably be needed
-Pry out the old seals...having a seal puller will be helpful...if not, punch them out from the other side with a broom handle
-Tap in the new seals
-Put everything back in...just be sure to put the carrier retainers back in exactly how they came out
You may have to get creative with getting those seals back in...broom handle and big socket from the opposite axle tube...you can get away with lightly tapping it in with a hammer, but be patient with it or you'll mash a seal. The tech manual says you need a special tool to get them back in...it basically presses them both in at the same time while you torque on it...but it's not necessary. There are some good videos on youtube.
A little bit of locktite on the outside of the seal won't hurt, but the wax coating (or whatever it is) on the seal itself will be plenty of a sealing surface if you don't have any locktite. It's just a little more insurance.
No need to check backlash or wear pattern if all you're doing is pulling the carrier and putting it back. You'll need to do that if you change bearings or spacers.