Are you referring to a washing machine standpipe similar to this but with the bluish part below the floor? Attachment 14008
If so, and if you are confident things have warmed up enough to have thawed the trap, then I would just keep the pipe topped off with tap water. A tiny trickle will dissolve away some salt. Once you have a little water through, adding more water for a while will get that salt all dissolved away.
Another variation is to suck out the top water with a turkey baster and refill with water. Avoid contact with the contaminated water. A wet-dry vacuum cleaner with a piece of 1-inch PVC pipe taped to the end of the hose could plunge in farther to get more stuff. Wash out the vacuum cleaner's tub when done to avoid hurting the vacuum cleaner with salt and lye. Top off with water after sucking what you can.
Adding some heat should help the melt, but don't start a fire.
If you have a dirt crawl space, consider going under the house with a small shovel and removing some dirt. Two person job... one to fill a bucket with the shovel, and one to haul the bucket with the attached rope to empty the dirt. That may be impractical, but it has been done by a lot of people.
I am not a pro.