Yes. I believe the difference is that the Kyrie tropes are written into the Missal already, while the Agnus Dei tropes were being composed by third parties and wedged in.
That’s correct, and the Kyrie has a long tradition of being troped, though Trent put that to rest. If you look at the current Graduale Romanum, the titles below each Kyrie, are the titles of the abolished tropes, e.g. Kyrie XI “Orbis Factor”. Some of the early tropes have been recorded including Orbis Factor:
The Missal gives sample invocations, but the priest is free to “wedge in” others.
Yep. The instructions for Option 3 for the Penitential Act includes the phrase “or other invocations.”
I think the opposite, rather. Historically, tropes were embellishments upon the texts of the Mass, not replacements for portions of them. Thus a trope on the Agnus Dei might say (and this is an actual example): “Agnus Dei, quem Iohannes in Iordane baptizavit ovans et dicens, ecce qui tollis peccata mundi, miserere nobis” (“Lamb of God, whom John baptized in the Jordan rejoicing and saying, behold: who takest away the sins of the world; have mercy on us”). So the variable invocations contemplated by Form C of the penitential rite seem to me to have more in common with traditional tropes than do the textual alterations which have frequently been practiced of late. Still, I think it better simply to call them, as the Missal does, invocations.
I guess the best thing is to judge for one’s self.
Those are the Christological tropes from the “Lamb of God” in Marty Haugen’s Mass of Creation, which was so widely used under the old translation that it would be safe to say that nearly-every U.S. Catholic knows those tropes (or “invocations” as Haugen calls them) by heart. In my experience, it was the only English setting of the old translation that I ever encountered with troped titles for Jesus in the “Lamb of God”.