Assalaamu wa alaikum
it returns as a curved sheath (singular). so the new moon is basically the zero moon or the astronomical new moon, which is before the crescent. when there is no moon in the sky.
the main problem is that the moon cycle is not a strict 29 or 30 days. rather 29.53 days. sometimes you will not see the new moon because the new moon might take place when it is day on earth, and by the time the sun sets, the crescent has already appeared.
if the moon returns as a curved sheath. then the next phase after the waning crescent is no moon in the sky, which can be easily confirmed through naked eye and telescope, where neither can contradict each other.
as shahr is something obvious it may be the phase when there is no moon, and it is obvious, even if you go to a mountain you won't see it.
as our calendar is similar to the scripture, the people of the book also use the astonomical new moon which is the zero moon to identify the new month.
Regarding the month of ramadhan, my opinion is there are a couple of definitions for the word ramadh, with i think shortness of rations predominating the heat interpretation.
if we denote rabi al awwal as the start of the grazing season, which starts in april, the grazing season finishes in autumn. there is shortness of rations as the trees shed their foliage. If we take rabia al awwal as april in the grazing season, then if we count down the months till ramadhan in order, we will find that it falls in october which falls in autumn.
in addition the word ramidha is used as a name in muslims and arabs and means white rose. As you know white roses or in general roses are particularly attached with autumn.
http://www.special-dictionary.com/names/r/ramidha_14.htmthat is why we have the famous " autumn rose "
As seasons are based on harvest, i would interpret ramadhan as ramidha or shortness of rations.
Salaam