For a quick fix... Axle is 100% right... you can just remove the spiders and leave the sides... just make sure you put the center pin back in! Also the washer that you found(?) can you give more detail on what it looks like? There are only a couple pieces that could be concidered "washers" the spiders and the side gears have a washer like component to keep them from binding on the carrier... then there are the Shims... those would be very easy to tell what they are... the Pinion shims are held in by the the pinion bearing race and cannot end up in the bottom of the diff. the carrier side bearing shims if you still have stock gearing are one piece, and pretty thick at that...
More info Please...
Thanks