Hey Tomas,
A couple affirmations...along with some additional.
1) Agitating the mash is very important for good BIAB efficiency. I agitate really well with potato masher when first mashing in, then twice in middle step of 90 minute mash, and again immediately prior to pulling bag and starting the boil Actually two mash agitations with middle step of reheating process at roughly 45 minutes, in middle of mash: a) agitate mash, b) pull bag partially / off the bottom of pot and reheat, then c) lower bag back into wort, then d) agitate mash again prior to e) re-covering pot with insulation... So I stir / agitate the mash at least 4 times total throughout the mashing process...very thoroughly.
2) Insulation - I wonder if your aluminized material will insulate enough...? Maybe. Just depends how cold it is outside. It looks really nice. Here is my process... A) use a cotton based blanket folded once lengthwise to wrap the pot with the excess folded and put on top the pot. B) wrap with similar size synthetic blanket folded same way. (Don't use synthetic against hot pot and burner.) C) wrap with old sleeping bag. Use a couple paper clamps to hold it on. I normally will lose 2-3 degrees during this time. And remember that if it is cold, a pot thermometer read from outside will likely be a couple degrees colder than the temperature in the middle of the pot.
Remember that "dead air space" is actually what does the insulating, and not the material that holds the "dead air"...
FYI Some people use a smaller size pot lid inside and at the bottom of their the pot, with holes drilled in it. Then don't cover the pot during the mash, using low heat and not pulling the bag... Then apparently pull the lid before the boil... I have no practical experience doing this.
3) Efficiency - the number on the BIABacus is always close. Plus or minus a couple points, with it being over more often than under. It is not some kind of vague number not to be achieved.
Certainly I remember the confusion of what to do, processes, when I was new. Asked a lot of questions on this forum and received great advice. There are multiple ways to get a good result. But if you are copying someone, it is best to model someone that is doing it right and getting the proper result. Best of luck and hope this helps!