THE ANALYSIS
For a better clearness, where necessary, we will refer as a topographic reference to the plan of the hospital shown in the pict.1: it is abstracted from the 1748 Nolli Map of Rome that, even if it is some decades subsequent to the events, offers the benefit of an excellent clearness.

Until the century XVII the hospital consisted of what should have become the Assunta Hall. In the Apostolic Visit of 1699 (see ref.A) it is indicated that its inlet was at the left of the Monastery (pict.3-a). With reference to the present arrangement, the old entrance of the hospital corresponds to the present entrance of the chemistry in front of St. Bartholomew square, while the entrance corridor to the Monastery is that just at the left of the St. Giovanni Calibita church (pict.3-b) once being its left nave.
The hospital hall, located at a level slightly higher than the roadway, is described as vault roofed and adorned with paintings; that corresponds to the structure of the Assunta Hall still visible today, in spite of the deep modifications occurred.
Besides the main entrance the hall had two more doors: one at the opposite end of the hall (visible in the 1676 Falda map shown in pict.4) and a third one that gave access to the cloister and therefore, according to the Nolli map, it was at about one third of the hall (pict.3-c). In front of this door, on the left wall, it was located an altar (pict.3-d).
In 1700 the hospital was restored by Carapecchia and in that occasion he  reorganized and renewed the Assunta Hall, the first modern hospital ward with 50 individual beds.
The completion of the Assunta Hall, and then its opening in the known arrangement, practically  unchanged until the restorations of the century XX, is dated on 28 February 28th 1702, corresponding to the visit of pope Clemens XI (also confirmed by ref.B1 e C1). As the visit occurred at 10 p.m., as quoted in the sources, somewhere we might find the next day date, March 1st, probably considering that in that time the change of date occurred at the sun sunset. Such event is  represented in the Painting 1 (ref.G1) as confirmed by the inscription made by friars on the back of the canvas.
Moreover it is commonly believed that the visit is represented in a painting formerly kept in the Fatebenefratelli in Milan and destroyed by bombing in 1943 (see ref. G2).
In that painting it is visible, behind the pope Clemens XI visiting the hospital, at the end of the hall, the altar with the image of the Assunta, to whom the hall is dedicated, and behind it of two semicircular stair flights that give access to a further elevated hall.

But in the same source C1 it is indicated that the pope, in that occasion, granted the small square behind the Hospital, (visible in the pict.4 map) in order to expand the hospital itself: it's just about the elevated hall (the future Amici Hall; see pict.3-e), that therefore was not yet built and cannot be represented in the painting.
This common mistake comes from the ignorance of the second papal visit in February 1705, event testified by the sources B and C (in particular see ref.B2 and C2) just recently recovered by the Author and Bro. Giuseppe Magliozzi (2005).
The painting should then refer, in all probability, to the second visit of Clemens XI, that on February 24th 1705 when the two semicircular staircases leading to the second hall, that frame the Assunta's altar, could be already completed (pict.3-f).

However in the ref.B3 it is indicated that in the August of the same year the Brothers of the  Fatebenefratelli invited the faithful to a contribute with charities for the building of the new hall in the area that the pope donated them for the purpose: this means that in that time the works for the Assunta Hall were not yet completed or, at least, those relevant to the second hall.
Moreover, comparing the Painting2 to the still visible elements in the hall (angels, drapery and, especially, the Assunta picture), one can noted remarkable differences that lead to doubt that the it was painted from life.
The most probable conclusion is therefore that the painting has been realized, on the basis of the sketch of the project, before the restoration of the hall, as thanks for the pope's donation in 1702, and shown to the pontiff in the occasion of his second visit in 1705.

In conclusion the restoration by Carapecchia of the main ward of the Hospital (the Assunta Hall in the strict sense of the word) can be considered completed in the very first years of century XVIII while it is still unknown the completion date in its final arrangement with the arch sustained by the angels, the Assunta's altar, the access flights to the new hall en the elevated hall itself. This event, anyway, can be dated not later than a few years after 1705.