The extra day of mattan Torah preparation added by Moshe

The gemara (Shabbos 87a) tells us that Moshe Rabeinu did three things ‘m’da’ato’, based on his own understanding, to which Hashem gave his consent. One of the three was adding an extra day to the preparation period before kabbalas haTorah. On Wednesday of the week preceding kabbalas haTorah, Moshe was told ‘v’kidashtem hayom u’machar’, to prepare ‘today and tomorrow’. Taken at face value, this would mean preparing Wed. and Thurs. for a kabbalas haTorah which would occur on Friday. Moshe, however, did not take the instruction to mean that. The gemara explains that he reasoned through a ‘hekesh’ that just like ‘machar’ includes a full day (meaning night+day), so too ‘hayom’ must be a full day (night + day). Since Wed had already started and would not be a full day of preparation, ‘hayom u’machar’ must refer to Thurs. and Friday. Hashem obviously consented with this addition of a day because kabbalas haTorah indeed did not take place until Shabbos morning.
There is a striking difficulty in this sugya which the rishonim and achronim address. We usually assume that anything derived through one on the 13 middot, which includes ‘hekesh’, is a din d’oraysa – the rules of derash reveal G-d’s command; they are not a means of superimposing Rabbinic law on the Torah text. If Moshe’s addition of a day was based purely on his insight alone, then he should not have needed the justification of a ‘hekesh’. And if Moshe’s addition was based on a ‘hekesh’, then how can that be called m’da’ato’, based on his own insight? He did not choose to add an extra day of his own volition, but was simply following the rules of derush to derive from the pasuk what Hashem intended all along?!
More to come…. (obviously, I’m getting a jump on preparing for Shavuos.)