K, let's break this down.
First of all:
(I will not account for the Energy you earn per run cause that’s based on luck)
That's a huge omission. People have logged literally thousands of runs, and the energy you earn back accounts for up to a third of the exp that you earn. So right off the bat you're saying "let's ignore one third of the exp you would earn by farming a scenario." Because you have a ZERO percent chance of earning exp while running secret dungeons, you're immediately trying to give the advantage to SDs instead of keeping things fair.
So let's go ahead and put that energy returned back in.
I'll use beathem's numbers (from here):
Faimon Normal: 780 * 3 / (3 - 0.94) = 1135 exp per energy
Faimon Hard: 1248 exp per energy
Faimon Hell: 1406 exp per energy
All we need to do to see if this is more efficient is see how long it takes to turn monsters into 3 stars. Because we know for a fact that it takes exactly 50 energy to get a 3 star from the SD (assuming you can 10/10 the SD).
To level a 2 star to level 20 takes: 35822 exp. Running Faimon one, on normal difficulty, without even using an exp booster it would only take you 31.5 energy to do that.
Holy shit! 50 energy to get a 3 star from the SD, or 31.6 energy to get a 3 star from Faimon one, on normal difficulty.
Ok, ok. Maybe starting with a 2 star is a stretch, afterall, we don't all have literally hundreds of unknown scrolls sitting around. Let's start with a 1 star monster.
To level a 1 star to level 15 takes: 15,120 exp. That's 13.3 energy from Faimon 1 normal, without using double exp. So the combined energy cost to go from a 1 star monster to a 3 star monster, doing Faimon 1, on normal difficulty, without a double exp booster, is 44.9 energy.
So there you have it. Doing Faimon 1, on normal difficulty, without an exp booster, it takes less than 45 energy to make a 3 star monster. That's 10% more efficient than farming an SD.
And if we actually brought crystals and refills and double exp into this, the SD gets beaten way worse.
Note that all of the above numbers account for raising 3 fodder monsters at a time and assume a single farming monster. So in the 1 to 2 star example, you're actually raising 3 one star monsters simultaneously, which results in making 3 2 star monsters for 40 energy, which comes down to 13.3 energy each.