Casey, in order to understand why what you want to do, is not a very good thing, you've got to understand a little about differentials and steering geometry.
When you're going around a turn, the wheels are turning at different speeds.
For example, say you're making a right hand turn.. The passenger side wheels are turning at a certain speed. The driver side wheels, because they have a larger radius to get from point A to B, are turning faster.
An 'open differential' like what you have now, allows the wheels to turn at different speeds. BUT, you only get actual 'power' driving one wheel.
Now, if you have a 'limited slip' rear end, you get actual power going to both wheels. This differential has (usually) like a little clutch and springs in it, to allow one wheel to turn at a diffrent speed than the other. Hence, 'limited slip'
("Sure-grip" in our case..)
So by welding up an open differential, your not allowing one wheel to turn at a different rate than the other.. So you'll get HARD streeing in the corners, wheel hop or chirping, scraping up tires needlessly, an possibly busting up the rear end and or axles into pieces.
Now if you plan on never doing anything but going in a straight line, have at it m'man!
