What is the meaning of "last day" from the perspective of the dispensational premillennialist?

You correctly speak of “Jesus' clear words that the resurrection of believers takes place on the last day. The Lord mentioned this promise several times. Even Martha reflects on Jesus' teaching: John 11:24 Martha replied, "I know that he will rise again in the resurrection at the last day."

In the Revelation Jesus gave to John via an angel, there is no ambiguity about “the last day” starting with “the last trump” – the fearsome angelic trumpet sound heralding the end of the Day of Salvation and the start of the Day of Resurrection and Judgment. Revelation 8 speaks of Christ opening the 7th seal, showing 7 angels being given 7 trumpets, blown by them in turn. Various plagues and afflictions fall from heaven on to the earth. Chapter 10 then says, “that there should be time no longer. But in the days of the voice of the seventh angel, when he shall begin to sound, the mystery of God should be finished, as he hath declared to his servants the prophets”. Chapter 11 says “And the seventh angel sounded;” vs 15, adding in vs 18, “And the nations were angry, and thy wrath is come, and the time of the dead, that they should be judged…” Chapter 20 makes it perfectly clear that that time of judging is when “the dead, small and great, stand before God”. Time is no more. The hour of judgment has arrived and ALL the dead are given resurrection bodies. This harmonises perfectly with what Jesus said about the resurrection happening on “the last day”, which Martha correctly understood would see her brother Lazarus arise from the grave, resurrected.

So, how can it be that dispensationalal premillennialists insist that there is a prior resurrection of Christians who will be taken up (‘raptured’) into heaven? It is point 2 in your “dispensational timeline” that requires explanation, and the most essential requirement for it is a secret rapture, requiring a two-stage return of Jesus Christ. This is where the following link needs to be checked, What scripture is used to support a "Pre-Tribulation Rapture"? to see the answer by Dick Harfield on 22/3/2015, for he cites a book that claims the origin of this idea was in 1830 when a 15-year-old Scottish girl called Margaret MacDonald attended a healing service, where she claimed to have had a vision of a two-stage return of Christ. Apparently this was adopted and amplified by John Nelson Darby, a British evangelical preacher and founder of the Plymouth Brethren. The book in question is called ‘The Rapture Exposed’, by Barbara R. Rossing.

To summarise Darby’s explanation, he has to claim that Christ returns secretly for his congregation, but that a literal angel appears in Rev. 4:1; that the voice saying, “Come up hither” into heaven, was spoken to Christians on earth – and they were raptured (dead Christians being raised first, the living ones following them up into heaven). However, given that ch. 4 is crystal clear that the voice like a trumpet was talking to John shortly before the end of the 1st century A.D., and that John was given a vision of himself being in heaven, such an explanation is insufficient (to put it charitably).

There is no mention of Christ having returned for the events in ch. 4, and no mention of any dead people having been raised. The phrase, “Come up hither” [to heaven] is interpreted as meaning a secret rapture of believers. An admission is made by Darby’s disciple, W. Kelly: ‘One important thing, then, we have seen to be assumed.’ He continues, ‘This most solemn and blessed event must occur therefore between chapters 3 and 4 of this book.’

The claim is made that the assembly of believers was seen on earth in chapters 2 and 3 but by ch. 4 the congregation is now in heaven, represented by the 24 elders. Thus, they conclude, there must have been a secret rapture (which didn’t happen to be mentioned anywhere, let alone in the chapter where it was supposed to have happened). Regarding Rev. 4:1 Darby admits, ‘There is no mention here of the fact of the Lord’s coming in reference to the assembly.’ That is why this dispensationalist, premillennialist system of interpretation claims virtually the whole of the rest of the Book of Revelation is irrelevant to Christians and only applicable to the Jews. It is only at ch. 20 that a sort of general resurrection is described.

Yet, as pointed out at the start of this answer, the Book of Revelation depicts the Day of Resurrection and Judgment, “that there should be time no longer. But in the days of the voice of the seventh angel, when he shall begin to sound, the mystery of God should be finished, as he hath declared to his servants the prophets” (ch. 10). Chapter 11 says “And the seventh angel sounded;” vs 15, adding in vs 18, “And the nations were angry, and thy wrath is come, and the time of the dead, that they should be judged…” It is not until the final, seventh, last trump that the awesome resurrection happens. Of course, I am not giving an answer in support of the dispensational premillennialist interpretation, but I offer this in the hope that some who do hold to such an interpretation might correct or enlarge.

Reference source for quotes by Darby and Kelly and summary of their view, ‘The Revelation of Jesus Christ’ by John Metcalfe, pp81-84 & p379 (The Publishing Trust 1998)