See http://www.hebrewbooks.org/pdfpager.aspx?req=16024&st=&pgnum=226
And specifically about the hiddur http://www.hebrewbooks.org/pdfpager.aspx?req=16024&st=&pgnum=233
I don't want to get dragged in here. So don't get me wrong, I am not addressing the rebbe, just what you post as your understanding of the minhag.
With all due respect, the Rebbe clearly explains that the reason you and the chasidim do not sleep in the succah is because of a petur of psychological tzar.
He does not address why you, who are "mehader" to eat in succah, even when potur because of real physical tzar, don't sleep. (Other than say that if the rebbeh didn't do it than you shouldn't even if his reasons of petur don't apply. This too is not sufficiently explained. How is it compared to a hiddur in haddasim..)
I don't understand how when you are "nebach potur" you call it a hiddur.
(Just btw, I happen to have recently learned, the inyan of psychological tzar. - imho it is pretty clear from the poskim that there is a chiyuv leyesuvey daatei in most cases... Interesting stuff)