Large old Steuben vase w/ scratches & cloudiness. How an I polish it?

To remove cloudiness try plain white vinegar - but don't let it sit too long. Just swish and dump.

Could use Jewellers Rouge, but am not hopeful.........

The cloudiness is from chemicals in the water. Use baking soda with a magic sponge. Damp the sponge and gently scrub. Since this is crystal, if the scratches and dullness don't come out after a couple of tries with the soda and sponge, do give it to a pro.

I would check to make it would not decrease the value before having anything done to it

Try vinegar and baking soda.

I use a bottle brush like you would use for a baby bottle to clean my vases.

Have you tried soaking it in vinegar and hot water?