Sawdust in a manual transmission?

Do you remember the old saying of doing this?
I'm assuming it had to be manual transmissions, would totally bugger up an automatic.
the reason I ask is I bought an old 4X4 Nissan. Loud roar when you get over 40mph.
I finally found the problem. The pinion gear in the rear axle is extremely worn. Ring gear too of course. The pinion is worn down to flattened faces of each tooth.
I've been searching for an axle. Thought i found one in Arkansas. Just talked to the man, he says apparently they have crushed and scrapped out the pickup his computer said was still in the yard.
Still looking. The one that's gone would have been $400 and 8 hours round trip to go and pick up.
I'm wondering if sawdust might quiet the rear end down and just drive the raskle till it dies.
Sweet little truck. I foolishly gave too much at $1250 for it. I was hoping the gearboxes were just out of oil.
Already replaced one front drive axle, $90. Ordered one for the other side......
4 cylinder. Could get 30-40 miles per gallon.
Am I throwing good money after bad? Park it and learn my lesson?
Or any possibility sawdust would quiet the rear axle to bearable levels?
Everything is in good condition. Motor is a transplant.
About 250,000 miles on the truck.