A good example of dispensational perspective is the first three chapters in the Revelation. Each of the seven churches were spoken to, with contemporary application to a particular ekklesia of believers and also for application to specific church behavior through the ages, and as descriptors for epochs of Church History. As such I believe we are in the Laodicean Age.
Using this dispy perspective it becomes clear that the Bible has many layers of God ordained messages for humanity and the two Testaments are intimately connected. I heard once (don't remember where the first time) that the in the Old Testament the New Testament is portrayed, and in the New Testament the Old Testament is revealed, something like that.
So, let's apply the two little tools above mentioned, to unpack your assertion:
'These "workers of iniquity" are those who wouldn't obey His command to "strive to enter in". Yes, He got the door open, but He ain't lettin' them in.'
We will look at to whom Jesus addressed His words, their reactions to His words, the subsequent reaction by Jesus to their repsonses, and finally the larger picture of Jesus's reason for taking flesh to dwell among us. There is definitely 'striving' for the Church Age believers, but it is not striving to enter the Kingdom, it is striving to follow the laws written on our hearts by His Grace and His Holy Spirit within raising us up in the way that we should go. Getting from newborn able to take only milk, to being able to take meat is not an easy thing for us since we retain the Adamic nature while in this body.
First, to whom did Jesus speak the verses you want to bring out for our inspection? when Jesus spoke of striving to enter in, He was referring to the period of human History, specifically Israelite History when striving to keep the laws of Moses was the means by which God was dealing with humanity. The source to show that differentiation is found in Acts 15, where the first church council is revealed in Jerusalem. Peter stands to address the dispute going on between the Pauline details of Gentiles being born from above into the Christian faith in Jesus, and the lack of following Mosaic laws to be born from above.
Pharisees among the church (I imagine Gameliel, Paul's teacher in Pharisaic office being one of them and perhaps Nicodemus, but that's grist for another mill) were insisting that new Christians should be circumcised and strive to follow the laws of Moses, all 600+ of them!
Acts 15 1&2 And certain having come down from Judea, were teaching the brethren — ‘If ye be not circumcised after the custom of Moses, ye are not able to be saved;’ there having been, therefore, not a little dissension and disputation to Paul and Barnabas with them, they arranged for Paul and Barnabas, and certain others of them, to go up unto the apostles and elders to Jerusalem about this question
When Peter stood to speak to the dispute he immediately focused upon the difference between the previous dispensation and the new one, the Old Testament covenant under the law and the New Testament covenant under Grace.
Acts 15:6 - 11 And there were gathered together the apostles and the elders, to see about this matter, and there having been much disputing, Peter having risen up said unto them, ‘Men, brethren, ye know that from former days, God among us did make choice, through my mouth, for the nations to hear the word of the good news, and to believe; and the heart-knowing God did bare them testimony, having given to them the Holy Spirit, even as also to us, and did put no difference also between us and them, by the faith having purified their hearts; now, therefore, why do ye tempt God, to put a yoke upon the neck of the disciples, which neither our fathers nor we were able to bear? but, through the grace of the Lord Jesus Christ, we believe to be saved, even as also they.’
So, Peter, to whom, as our Catholic friends are quick to point out, Peter carrying the keys to the Kingdom gives a short version of the New Covenant participants, Jews and Gentiles, both brought into the Church, the body of believers in Christ as Messiah and Lord via Peter preaching The Gospel of Grace. In the New Covenant there is no distinction between Jew and Gentile for all in His Church are under His Grace by His Grace not their adherence to the laws.
Peter's short explanation also contains a vital clue to differentiate the previous covenant from the New Covenant, and it is precisely what you've raised for discussion: striving, striving to keep the laws. It is this means to interact with God that God, in the Person of Jesus Christ, has given a New way to interact.
To fully comprehend the vitals of this new covenant relationship between Man and God we would need to unpack the Epistles of Paul to the various ekklesia gatherings he established via his missionary journeys. In the interest of brevity I will cite a few which run as themes through his letters.
Paul declares that it is by faith we are saved not by works [Letter to the Romans] ... not by striving. Striving was the hallmark of the covenant of the laws. The Old Testament Prophet, Jeremiah, revealed how God would upgrade that covenant for a new covenant where the laws reflecting the character of God would be written on the hearts and not need to be on stone tablets.
Hebrews 10:16 This is the covenant that I will make with them after those days, saith the Lord, I will put my laws into their hearts, and in their minds will I write them; {Jeremiah 31:33]
I tend to be long winded, so I'll pause here and see if this is coming in clear for you. Then we will continue from this Church Council in Jerusalem.