If you dig into the world of social media you will discover that at least two members of the team (M. Lefantzis and Antonio Corso, the second being the expert for studying the sculptures) are quite open with providing info regarding the monument. From that and Peristeri's and Lefantzis presentations one can understand where some, if not most, of the info about dating comes. I try to provide a summary below. What is unfortunate is that K. Peristeri makes rather bad presentations, her speeches are careless and never tries to make a clear separation of data and hypotheses. It is interesting to view her slides but difficult to understand her explain them. Having that limitation, I just try provide below what I understand the team claims - some guesswork is involved but no personal opinions:
1) Lion: dated as a 4th century BC sculpture by the team as well as most other experts. If it was on top of the Kastas Hill (see points 2-7), that at least dates the intent of the designer to have a monumental construction at Kastas. Whether that was completed on the 4th century BC or later is another story.
2) The parts of the Lion that were discovered by the Greek army and later on by English forces were originally scatter in a 4 km wide area extending towards Kastas. Part of the lion's back was discovered by the current investigators close to Kastas, part of the lon's mane was found at Kastas (it was even mentioned in a press release). Tons of marble piecies were discovered at the top of Kastas's hill by Lazarides, when he was excavating there in the 1970's, indicating the presence of a large marble monument, where the foundations of a ~10 m x 10 m base were found.
3) The frieze attributed Lion's base was discovered near Kastas in the 2012-2013 excavations. Many parts of it were found integrated in late roman or Byzantine constructions at the acropolis of Amphipolis. This was actually presented in the 2013 or 2014 conference about progress in archaeological studies in Macedonia and Thrace, although images did not go public. The workmanship on these pieces helped, among other, in order to identify them. What they also state is that iconography of the frieze is consistent with a late 4th century BC dating. I assume geometrical features of the frieze (one piece is very large) or other aspects (e.g. locations of clumps etc.) are probably also helping with its association to the base of the lion.
4) Roger, Broneer and Millers studied the marble remains of a large construction near the Strymon. Among the pieces we now know belonged to the peribolos, they also found several parts with shields and columns that had common elements - so they likely came from the same construction. Millers propose a reconstruction of this monument (and give litte margin of error for this reconstruction) - it came out to be a square building with approximately 10 m wide on each side, very close to the sizes of the foundations found on top of Kastas.
5) Most or all authors above mention that the workmanship on the peribolos blocks is similar to that of the 4th century BC lion and proposed they may come from the same monument. That is why for instance Roger or Broneer in the proposed reconstruction of the lion assumed that the peribolos blocks formed parts of its base (and that is why many peribolos blocks are actually used).
6) Millers proposed a dating of the peribolos blocks to either 4th or 2nd century BC. Bakalakis proposed a 2nd century BC, Roger/Broneer a 4th century BC. From all the above it seems a 4th BC dating is what makes sense
7) There are geometrical aspects of the discovered lion parts (e.g. gap between the feet) that match features discovered within the foundation on top of Kastas. Specifically, it is assumed that a hole located by Lazarides was used to position and stabilize the lion.
8) "ANT" monogram on the peribolos. Does not support 4th century BC dating, only considered as an indication that the peribolos is Hellenistic
9) Letter bundle with (almost?) all letters of the word "ΗΦΑΙΣΤΙΩΝΟΣ" in 2 or 3 peribolos blocks. M. Lefantzis claims that workmanship reveals that the inscription that contains the bundle was written before its final processing for placement on the peribolos. When combined with everything else + the large size/luxury of the monument, the bundle is attributed to Hephaestion, which then supports the dating.
10) The Caryatids wear sandals of the late 4th c. BC (the date of this type of sandals has been established by Froning in 2007)
11) Surfaces of Caryatids and Sphinxes are crispy, as it is typical of late classical sculptures, and not hyperpolished and translucid as it is typical of late Hellenistic sculptures.
12) The arrangement of the drapery of the Caryatids - with an oblique strap anda a triangular pattern with a zig-zag decoration - is exactly corresponding with the same patterns on a statue of Dionysus from the theatre of Euonymos which is epigraphically and archaeologically dated around 330-320 BC.
13) The wings of the Sphinxes are of the typically late classical large size and not yet of the reduced size which became trendy after the Eros and the Kairos of Lysippus.
14) Bases of Caryatids are not decorated - as it became usual for later hellenistic times
15) Reference 4th century BC art/sculpture works (by Antonio Corso) :
https://www.facebook.com/antonio.corso. ... 1311717165
16) Note by Antonio Corso: "one of the indices to date a female sculpture is the way breasts are carved. In the period of the severe style, there is a wide bosom between the two breasts, the bosom is already reduced with the Cnidian Aphrodite, it becomes very narrow with the Capitoline Aphrodite, whose original statue was created toward the end of the 4th c. BC. The width of the bosom of the female sculptures of Amphipolis is similar to that of the Cnidia, and this is one of the many reasons which lead to a date of these sculptures before the creation of the Capitoline Aphrodite.
This sequence is not a new discovery. Already Reinach understood this trend in carving breasts in his article 'L'indice mammaire' of 1931."
17) Mosaic with geometrical patterns before the caryatid entrance: same as a 4th century mosaic discovered ~200 m south of Kastas (although some date it down to early 3rd century). Comparisons also with Pella and other placed support the 4th century BC dating
18) Pebble mosaic technique - used up to mid 3rd century BC, becoming mixed with other techniques later.
I dont think coins or ceramics from the tomb have been used to date anything, other than approximate the period the tomb was sealed (by just looking the latest date of those finds). E.g. 4th century BC Alexander coins found may have entered there by accident with the earthen fill.
19) Decorative parts of the klinai found at the 3rd chamber also consistent with a 4th century BC dating.
Apart from that, it is also my understanding that it is only claimed that the original purpose for building the monument was to use it as a heroon for Hephaestion - that is based on their interpretation of the inscriptions. There is no claim, to my knowledge, regarding the stage at which the monument's use was changed. Maybe the Hephaestion heroon idea was abandoned even during construction, but construction continued maybe for the benefit of Antipater or some other reason.
Also, I think the association with Monophthalmos is problematic, they just try to explain how the monogram appears at the peribolos while being consistent with a 4th century BC dating. Regarding the inscriptions, I am at least sure that they have nothing to do with the much later graffiti on the blocks which is very deeply carved and contains only names - not actions. I have no opinion about dating sculptures, my only understanding is that while arguments presented by A. Corso appear reasonable to a non-expert, he cares mostly to explain why the sculptures are not late-hellenistic or roman. I don't see how his arguments exclude an early 3rd century BC dating. It appears that the strongest dating argument so far comes from the association of the lion with Kastas and the common processing elements found with the peribolos blocks and the (candidate) base pieces.