In a heavy saucepan, simmer apricots, water, and 1/2 cup of the sugar, covered, for 20 minutes. Transfer hot mixture to a food processor and puree until very smooth. Force puree through a fine sieve into a bowl and stir in the lemon juice, rum, vanilla, and 1 pinch of salt. Cool puree completely. (Puree may be made 2 days ahead and chilled, covered.) Bring puree to room temperature before proceeding. Transfer puree to a large bowl. Preheat oven to 350 degrees F. Generously butter six, 7-ounce (3 1/2 by 1 3/4) ramekins and coat with additional sugar, knocking out the excess. With an electric mixer, beat whites with a pinch of salt until foamy. Beat in cream of tartar and beat whites until they hold soft peaks. Beat in remaining 1/4 cup of sugar, a little at a time, and beat meringue until it just holds stiff peaks. Whisk about one fourth of the meringue into the puree to lighten, then fold in remaining meringue gently but thoroughly. Ladle batter into ramekins and bake souffles on a baking sheet in the middle of the oven for 20 to 25 minutes, or until puffed, golden brown, and just set in center. Remove ramekins from oven. Whisk heavy cream until doubled in volume, add rum and continue to whisk until light and fluffy. With 2 forks pull open center of each souffle. Place a dollop of rum-laced whipped cream in opening.