No, there's no false dichotomy presented in my statements, only the dichotomy Jesus himself put forward.
Matthew 7:13-14
13 “Enter by the narrow gate. For the gate is wide and the way is easy that leads to destruction, and those who enter by it are many.
14 For the gate is narrow and the way is hard that leads to life, and those who find it are few.
Jesus did not restrict his meaning here to Jews only. This restriction you must force into his words, not draw out of what he said. Simply by adding "of you" to his statements, Jesus could have confined his meaning to his audience in the way you suppose he had: "...those of you who find it are few." But, as you can see, he didn't. His remarks about the many on the Broad Way and the few on the Narrow Way are completely unqualified.
Only if I'm importing into Scripture a universalist view is it necessary to force Jesus' words above within boundaries amenable to the view. Doing this, doing eisegesis, with Scripture is a very bad practice.
Is there some other place in God's word that would serve as good ground for the restriction you're wanting to force upon Jesus' words? The only other passage that might offer such ground is the following from Luke's Gospel:
Luke 13:23-30
23 And someone said to him, “Lord, will those who are saved be few?” And he said to them,
24 “Strive to enter through the narrow door. For many, I tell you, will seek to enter and will not be able.
25 When once the master of the house has risen and shut the door, and you begin to stand outside and to knock at the door, saying, ‘Lord, open to us,’ then he will answer you, ‘I do not know where you come from.’
26 Then you will begin to say, ‘We ate and drank in your presence, and you taught in our streets.’
27 But he will say, ‘I tell you, I do not know where you come from. Depart from me, all you workers of evil!’
28 In that place there will be weeping and gnashing of teeth, when you see Abraham and Isaac and Jacob and all the prophets in the kingdom of God but you yourselves cast out.
29 And people will come from east and west, and from north and south, and recline at table in the kingdom of God.
30 And behold, some are last who will be first, and some are first who will be last.”
So, two things stand out from this passage in regards to the universalist view:
1.) Many will not be able to enter through the Narrow Door (vs. 24), but will be shut out by the Lord, cast out of God's kingdom into a place where there is "weeping and gnashing of teeth" (vs. 28)
2.) Jesus spoke, not solely of Jews, but of people from all four directions of the compass (a figurative way of saying "from everywhere" - vs. 29). Luke confirms, then, in his account of Christ's words above that, in Matthew 7:13-14, Jesus did not restrict his remarks to Jewish folk.
So, then, I haven't put forward a false dichotomy, but the dichotomy Jesus himself established between the many who follow the Broad Way to Destruction and the comparatively few who follow the Narrow Way to Eternal Life.