Look at pretty much any introductory text on QM and the Copenhagen interpretation (or the "orthodox" interpretation) is presented as an objective collapse theory, with collapse being a physical process that takes place upon measurement.

That is perhaps a common misconception in popular science publications aimed at non-technical audiences, but I'm not aware that it's prevalent in technical literature. Even if it was, that's not a good reason to further the misuse of terminology.

As for your point 2, it just isn't true that all collapse interpretations assume that collapse only takes place at the end of the experiment.

It doesn't matter. All interpretations must agree with the predictions of the theory, at least in all the cases that have been practically testable so far. The experiment you proposed predicts the same results whether or not you shield the intermediate observer from decoherence. If your math predicts different results, then there must be some mistake in it.

Also, if collapse is supposed to take place only at the end of a measurement, how do objective collapse theories make sense of phenomena like the quantum Zeno effect, where measurement is taking place continuously throughout the course of the experiment?

Why wouldn't it make sense of it?