There is one harvest at the last trump (which is the end of the age) but two reapings. The one harvest is called "the harvest of the earth" - Rev. 14:15. The first reaping is when the Lord of the Harvest gets his "good wheat gathered into his barn". Only after that do angels go forth to gather the grapes of wrath for treading down in the wine-press of the anger of God. That is spoken of as gathering "the clusters of the vine of the earth" - Rev. 14:17.
Study of Leviticus 23:10-11 will give the understanding of the firstfruits of the wheat harvest; the first sheaf was "cut off from the earth", answering to the day of the passover in the type when Christ hung on the cross. The morrow after the sabbath, namely, the first day of the week, the firstripe sheaf was waved by the priest before the Lord. From that day, 49 days were counted before the main harvest was begun. The full fullfilment of all that comes at the reaping of the harvest in the last day. Compare Matthew 3:12 & 13:39. After the reaping of the first token sheaf of wheat comes the main harvest of the rest of the wheat, 49 days later. In Revelation 14, the second reaping comes:
"after the reaping of the harvest of the earth - it is called by
another name. That name refers to the clusters of the vine of the
earth... This implies that the wheat harvest, as opposed to the
gathering of the grapes of the vine of the earth, is an entirely
separate event: the two representing as different a form in
agriculture, as do the sheep and the goats in nature.
"Therefore, the appearance of another angel having a sharp sickle in
his hand, cannot possibly be in respect of that harvest of the
firstfruits already reaped by one like unto the Son of man, though the
gathering of the grapes follows instantly... to bring in that which is
left on earth after the reaping by the Son of his own harvest." (The Revelation of Jesus Christ, pp 403-7, John Metcalfe, selections)
A hermeneutic point is about two different words that can be used for 'sickle'. A sickle is used for the harvest of wheat to be safely gathered in before another sickle is used to cut the vine. The significance is explained in the same book:
"There are two words in the Hebrew for 'sickle'. The first is
chemesh, Deuteronomy 16:9, 'Begin to number the seven weeks from such time as thou beginnest to put the sickle [chemesh] to the
corn'. This agrees with the reaping of the firstfruits by the Son. The
second word is maggal, 'Let the heathen be wakened, and come up to
the valley of Jehoshaphat: for there will I sit to judge all the
heathen round about. Put ye in the sickle [maggal] for the harvest
is ripe: come, get you down; for the press [that is, the winepress] is
full, the vats [of the winepress] overflow; for their wickedness is
great" Joel 3:12, 13. This agrees with the second, angelic, reaping;
the gathering of the grapes of the vine of the earth." (Ibid.
This point helps confirm that one sickle is used for the first gathering (of the wheat of the earth) but a different one for the second gathering (of the vine of the earth). This indicates that the two reapings cannot go on simultaneously.
To answer your question, based on explanations in that book (far more than I can put in my answer here), it would seem that "these harvests be considered as being done sequentially (first the holy wheat, and then the grapes of wrath)", as you put it in your comments.