Would it be better to remove the cover and reseal with RTV or just use a pump to suck the old gear oil out?

Also, if I do remove the cover, what's the best way to clean all the gunk out of the inside of the cover?

I have done a search, and yes, I found results, I really didn't find what I was looking for.

I would remove the cover & drain out all the old fluid. It would give you an opportunity to examine the condition of the gears. You should be able to simply wipe down the diff cover prior to reassembly.

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my trail & highway ride (and occasional tow rig)
04 Liberty Sport with a 2.5" lift, ProComp 245/75R16 AT's and two Hella700FF lamps (more accessories to come)

my trail queen
95 YJ with a RE 4" lift, 33" ProComp Extreme's, M8000 Winch, Lockrite Locker up front, Super35 in the rear and 4.88 gears

Pull the cover. Clean the mating surfaces with a razor blade or scraper, but be careful not to score the metal. Use brake cleaner to clean out the grey stuff in the diff and on the cover. Let the brakleen dry, then put a good bead of differential RTV (yep, there is specific stuff) on the cover, looping around the bolt holes. Put cover on, tighten the bolts halfway. Let the RTV set up for 30 mins, finish torquing the bolts (be careful - do NOT over-tighten). Let the RTV cure another 30 mins (not necessary, but I like to be careful), then fill with good diff fluid.

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2005 Liberty Renegade, Bright Silver Metallic

Do I put RTV on the plug too? It looks like a rubber push plug from what I can tell. I sits pretty flush against the diff cover.

No.

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2005 Liberty Renegade, Bright Silver Metallic