It also doesn't get around the issue of the fact that the sheep and their shepherds weren't still out in the field come December due to it being Israel's rainy season, and being pretty darn cold up in the mountains. To quote Adam Clark:
It was a custom among the Jews to send out their sheep to the deserts [wilderness], about the passover [sic], and bring them home at the commencement of the first rain: during the time they were out, the shepherds watched them night and day. As the passover [sic] occurred in the spring, and the first rain began early in the month of Marchesvan, which answers to part of our October and November, we find that the sheep were kept out in the open country during the whole of the summer. And as these shepherds had not yet brought home their flocks, it is a presumptive argument that October had not yet commenced, and that, consequently, our Lord was not born on the 25th of December, when no flocks were out in the fields; nor could He have been born later than September, as the flocks were still in the fields by night. On this very ground the nativity in December should be given up. The feeding of the flocks by night in the fields is a chronological fact, which casts considerable light on this disputed point. (Clarke's Commentary, vol. V, p. 370)Shalom.
Well, as I understand it the explanation given is that the disruption goes all the way back to the return from Babylon. For your scheme to work the timing would have had to remain intact going all the way back to the time of Chronicles. The Jewish record of the 1st century suggests that was not the case.
But Edersheim has 5 other points to support his conclusion. And he is certainly not alone. A number of authors after careful researched have concluded that while we cannot know for sure, the traditional date is quite possible.
consequently, our Lord was not born on the 25th of December, when no flocks were out in the fields; nor could He have been born later than September, as the flocks were still in the fields by night.
Actually, there is good historical evidence to suggest that flocks would have been present as specified in the gospel account in the December period. Again, quoting Edersheim:
But as we pass from the sacred gloom of the cave out into the night, its sky all aglow with starry brightness, its loneliness is peopled, and its silence made vocal from heaven. There is nothing now to conceal, but much to reveal, though the manner of it would seem strangely incongruous to Jewish thinking. And yet Jewish tradition may here prove both illustrative and helpful. That the Messiah was to be born in Bethlehem,949 was a settled conviction. Equally so was the belief, that He was to be revealed from Migdal Eder, ‘the tower of the flock.’950 This Migdal Eder was not the watchtower for the ordinary flocks which pastured on the barren sheepground beyond Bethlehem, but lay close to the town, on the road to Jerusalem. A passage in the Mishnah951 leads to the conclusion, that the flocks, which pastured there, were destined for Temple-sacrifices,952 and, accordingly, that the shepherds, who watched over them, were not ordinary shepherds. The latter were under the ban of Rabbinism,953 on account of their necessary isolation from religious ordinances, and their manner of life, which rendered strict legal observance unlikely, if not absolutely impossible. The same Mishnic passage also leads us to infer, that these flocks lay out all the year round, since they are spoken of as in the fields thirty days before the Passover - that is, in the month of February, when in Palestine the average rainfall is nearly greatest.954 A somewhat different explanation is given in Jer. Bezah 63 b. Thus, Jewish tradition in some dim manner apprehended the first revelation of the Messiah from that Migdal Eder, where shepherds watched the Temple-flocks all the year round. Of the deep symbolic significance of such a coincidence, it is needless to speak. ( Life and Times of Jesus the Messiah, Chapter VI)949 In the curious story of His birth, related in the Jer. Talmud (Ber. ii. 3), He is said to have been born in ‘the royal castle of Bethlehem;’ while in the parallel narrative in the Midr. on Lament. i. 16, ed. W. p. 64 b) the somewhat mysterious expression is used {hebrew}. But we must keep in view the Rabbinic statement that, even if a castle falls down, it is still called a castle (Yalkut, vol. ii. p. 60 b).
950 Targum Pseudo-Jon. On Gen. xxxv. 21.
951 Shek. vii. 4.
952 In fact the Mishnah (Baba K. vii. 7) expressly forbids the keeping of flocks throughout the land of Israel, except in the wilderness - and the only flocks otherwise kept, would be those for the Temple-services (Baba K. 80 a).
953 This disposes of an inapt quotation (from Delitzsch) by Dr. Geikie. No one could imagine, that the Talmudic passages in question could apply to such shepherds as these.
954 The mean of 22 seasons in Jerusalem amounted to 4.718 inches in December, 5.479 in January, and 5.207 in February (see a very interesting paper by Dr. Chaplin in Quart. Stat. of Pal. Explor. Fund, January, 1883). For 1876-77 we have these startling figures: mean for December, .490; for January, 1.595; for February, 8.750 - and, similarly, in other years. And so we read: ‘Good the year in which Tebheth (December) is without rain’ (Taan. 6 b). Those who have copied Lightfoot’s quotations about the flocks not lying out during the winter months ought, at least, to have known that the reference in the Talmudic passages is expressly to the flocks which pastured in ‘the wilderness’ ({hebrew}). But even so, the statement, as so many others of the kind, is not accurate. For, in the Talmud two opinions are expressed. According to one, the ‘Midbariyoth,’ or ‘animals of the wilderness,’ are those which go to the open at the Passovertime, and return at the first rains (about November); while, on the other hand, Rabbi maintains, and, as it seems, more authoritatively, that the wilderness-flocks remain in the open alike in the hottest days and in the rainy season - i.e. all the year round (Bezah 40 a). Comp. also Tosephta Bezah iv. 6.