STEAM CLEANING LP's

Be careful about applying too much steam too long if it is for heavy duty use. It may cook the LP. I ruined about 5 of my LPs with my garment steamer. 4 of them old/junky but 1 in close to new condition. Ouch!
Try first with a junk LP.

Does anyone have a good method to protect the label from mist or splatter?

mist or splatter protection is best solved by using a shield that was available on line for that exact purpose. I have one, don't remember its name. It is two shields that screw on to the record, covering both sides with a tight seal. It is acrylic with two o rings. Others must have one and they might remember its name. I recall it being about $30. I really does the job, especially if you using steam.

Hopefully someone knows the source.

You can get that shield on ebay, but I forget the name.