Here is the approach I used at [Cong] Mt. Sinai -
Moshe was not given all 613 mitzvos at Mt. Sinai per se. This is in apparent contrast with Rashi in the opening of B'har 25:1
Rather Moshe was given some Mitzvot in detail on Sinai and Hashem told Moshe:
"Moshe when all is said and done there will be a total of Taryag Mitzvot altogether "
But Perhaps HKBH never enumerated them and therefore allowed them to unfold.
Thus, the Sum Total of 613 is indeed a tradition from Mt. Sinai, but not necessary any enumerated list
This addresses all the above questions. And it was only the Rambam who first concerned himself with a DEFINITIVE list. Until then, while the total was axiomatic, the enumerations thereof were in flux.
For an alternate, but radical, hypothesis -
613 were literally given at Mt. Sinai [opening Set]
And those Mtzvot given in the Midbar at Ohel Moed were NOT included. [2nd Set]
Note: That might include all given in the Midbar, or may be limited to only those originating in the Midbar W/O roots from Sinai
At any rate, the 613 later encompassed both sets somehow
I also highly recommend this book by
Abraham Hirsch Rabinowitz
TaRYaG: a study of the tradition that the written Torah contains 613 mitzvot