We're so glad this post could be of help, Ahuva! We, unfortunately, don't work with sugar replacers in our test kitchen so usually, the best tips on using those come from the brands' websites. But we can certainly answer your other questions! The good flavors that come from refrigeration will still be there if you let the dough come to room temperature. The egg does add some moisture along with wonderful tenderness thanks to the fat from the yolk. It also lends some strength and structure from the protein of the egg white. Normally for a crispier cookie, we suggest replacing brown sugar with white sugar so that may be a bit trickywhen working with sugar replacers without some trial and error. 

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