In large glass bowl, combine all vegetables and salt. Cover and set aside at room temperature 3 hours. In colander, drain vegetables. Rinse quickly with cold water and drain very well.
In large non-aluminum kettle, combine vegetables, vinegar, sugar, mustard seed, and cayenne. Bring mixture to boiling over high heat, stirring constantly. Reduce heat to low and cook, uncovered, 20 minutes, stirring occasionally.
Meanwhile, sterilize 4 pint jars, lids, and bands according to manufacturer's directions. Divide Piccalilli among sterilized jars leaving 1/2-inch space at top of jar. Wipe rims of jars to remove any syrup and seal with lids and bands.
Process jars in boiling water bath for 10 minutes. Remove jars from water bath, tighten lids immediately, and set aside to cool completely. Label jars and store in cool, dry place.
If green tomatoes are unavailable, substitute underripe red ones and, for color, substitute 1/2 pound of green peppers for 1/2 pound of the red ones