Grease in rear end?

OK my wife has an 02 Explorer. I know it doesn't really fit in the rat rod forum but I need some advice. I have done a lot of internet searching on this. Mostly I just hear people complaining. It has a whine coming from the rear axle. This has been going on for a while. Sounds like I'm running mud tires on the thing. I replaced the tires awhile back and noise continued. Checked the rear oil level and it was low (and leaking). It leaks at the 3rd member axle tubes (independent rear). My options are completely remove axle assembly and replace with Pullapart junkyard axle. Completely rebuild or try and ignore. I have heard people rebuild these multiple times and still have problems. When I first bought this truck I had the rear bearings replaced by Carmax as it was under warranty. It wasn't whining at the time but was making a strange noise. Never was really fixed properly but they said they did all they could, after taking it to them multiple times.
I had a Honda Goldwing with a leaky final drive and the guy I bought it from said his mechanic told him to put grease in it and it would be fine, still leaky but not as bad.

My question is does anyone think putting a high temp bearing grease in the limited slip rear would be ok?

I don't want to cause more problems than I'm "fixing". I know this isn't a permanent solution. I think it may be leaking at the outer seals and bearings now to. Sometimes after a drive you can smell the gear oil burning . In the end I will have to put a "new" axle in. Just looking for a temporary "fix". Until I replace the axle assembly, or buy something else. I still owe 8k on this stupid thing. Trying to convince her to let the thing go and go pay 4k for something cash. Already had to let my work van go (lack of work) and have credit card collectors after me. What's one more?

I see you posted this a week ago so by now you have probably made repairs but I'd like to comment anyway.
You have a serious problem and shouldn't drive the car. If the gear lube is getting hot enough to "smell" hot it could actually catch fire and destroy the vehicle not to mention the personal danger to you or your wife. Best budget fix would be the junk yard part. Hope you got the problem fixed and will let us know what you did.

The gear oil is burning on the exhaust. Leaking from the 3rd member. I don't think the outer seals have any problems. Haven't looked really good yet, but it looks like I have to remove the axles (independent rear) to even get the assembly out. Looks like the axles go over the frame. So even if I got a junkyard axle it would some new seals, etc. I went ahead and put grease in it. My wife says it seems quiter. I'm ether going to see what happens, pay 1500 to 2500 to have a mechanic fix it, or buy something else. I don't feel comfortable enough to rebuild the one in it quickly. I don't have the time or patience to do it myself. And I don't need the headache. I hate working on newer cars. Everything is over engineered and a pain in the you know what.

my boss has one that has the same problem none of us or the dealer can fix it so run it till it breaks, they have been running theirs for about 6 years are so.

odie

ford rear diff

these rear diffs are bad about spyder gears going out, for some reason they get pits in them, ford sells a complete spyder gear kit, they are not that bad to replace, bset to pull the thrid member all the way out, put the new spyder gear kit in and new side seals, that rear diff will also use 75w140 syn. gear oil also and a 4 0z. bottle of friction modifier, take your time and you should have no problems, its just nuts and bolts !