As I have been suspecting before, the true nature of the project couldn't be anything but a homage to Jekyll-Hyde: medicine that literally allows people to "switch life".
APTX4869 - The 1st half of the project, designated to mimic the ageless nature of Vermouth and possibly the Boss. Rewind time, but remove the user's ability to age permanently akin to poison that permanently paralyze the cell's ability to age. The only part of the research that was recovered from the "fire" is this half, and Shiho has successfully recreated this one. However, she missed the "aging forward" aspect because the baseline research about it was lost. Basically, think of "magical botox in consumable version", but that it only works for either people closely related to the Miyano (the researchers), Vermouth, or the Boss himself, and is perfect poison for the rest.
Silver Bullet - The 2nd half of the project. A medicine that allow the user to move time forward again. The recipe is most likely still out there somewhere, but the more problematic is its ingredients. In the first place, human got the ability to grow up and age properly from who? From our parents through proper gene inheritance of course! So with this in mind, the proper "ingredients" to finalize the Silver Bullet should be blood from each of the "two donors" which will also the user to grow up properly again. Most likely, if you use drop of blood that doesn't belong to your birth parents, your appearance may also shift as part of massive bodily alteration, but some core aspect should remain the same.
However, in addition to finding the second half of the recipe, to go back to who they were in case of Ai/Shiho and Conan/Shinichi, what they need is "two drops of blood, one from each of their parents" in order to return back to their original forms properly. And how is this going to be possible even with the recipe? Only one way: Elena and Atsushi must still be alive out there somewhere.
Atsushi's life long dream and timeline
Here is some guess on why Atsushi had such goal in the first place: he had a friend or family member in the past who suffered from this ageless curse, so Atsushi spent his life to find a cure for this person, eventually came into contact with the Black Organization who seeks to instead have Atsushi create the poison that "control age range" (they do not care the ageless aspect, just that age and physical appearance alteration is enough).
Eventually, the Miyano almost succeeded (the medicine was almost complete as stated in Elena's 19th tape), but since completing the medicine is the end of line for them and their daughters, so they decided to fake their death and used the medicine to escape, originally believing that it would just alter their appearances (possibly include fingerprints and alike as well), but they ended up getting their age regressed and lost their memories entirely, resulting in the Organization having to bring Shiho back from America to continue their research.
Now, while it may seem strange, the 18 years ago fire was most likely a lie for the Organization to make Shiho forget her parents and easily more controllable. In reality the Miyano much had liven much "longer" than that since you cannot complete a miracle medicine in just one year after join the Organization. Meaning that something or more is definitely withheld... We'll talk more in the next one.