The laser goes through the bagel hole each time until it hits the ground (assuming the mirrors are set up nicely orthogonal to your uniform gravitational field).
To see why, the equivalence principle is all we need. You can imagine thrusters powering an elevator without gravitational fields, set up your mirrors and do the experiment, and that's what you get.
But what about the doubling of the deflection? Einstein originally used the equivalence principle alone to predict a deflection of light that was half what he predicted later using full General Relatvity. I just used the equivalence principle alone. Did I repeat a mistake? No. Einstein's original calculation neglected the spatial curvature, specifically the fact that the curvature was different from place to place. So Einstein's original calculation is exactly what we need for your uniform field situation!
The bounty was for well-cited answers. Mathpages is accessible. You can pick up a textbook on General Relativity, such as Chapter 18 of Schutz’s Gravity from the Ground Up (which is historical and modern and practical and both algebra and calculus based if I recall correctly) or chapter seven of Clifford Will's Theory and Experiment in Gravitational Physics. And here is a review of Einstein's Review article of 1916 (the one where Einstein correctly predicted the deflection) Review of Albert Einstein's 1916 Review Article on General Relativity
So that's the answer, the reason, and citations. But I also want an answer to be maximally educational, so let's put everything in a proper perspective.
General Relativity has a Newtonian Limit. In that limit it is the time-time part of the curved metric that gives the biggest effect (and the only surviving effect if all the otehr effects get smaller and smaller enough which happens in an extreme newtonian limit). The newtonian limit happens far from compact sources, it happens also at low speeds (we are trying to get newtonian here), and you need both the weak gravity and the slow motion to get the newtonian limit. Historically this is originally what Einstein was computing because he was finding the effect of the time-time part of the curved metric from the equivalence principle.
Now, sometimes the newtonian limit doesn't hold, there could be strong fields (large rotation, nearby compact mass, etc.), there could be fast motion. Light is always fast, there is no way around it. So you can't use the newtonian limit for light, and the variation of the spatial curvature then becomes important. When Einstein took that into account, that's when he got the twice the deflection result.
So to summarize:
1) In a uniform weak field, the equivalence principle is fine, gravity and acceleration are basically the same.
2) The newtonian limit is based on the curvature of time, not of space.
3) When there is spatial variation of the curvature that can't be ignored (such as a nonuniform field and fast motion), then other curvature (such as spatial curvature and its variation) matter.
4) A strong field can be strange too, there can even be strange effects, like an Unruh effect making a Geiger counter tick in empty space when accelerated by an elevator. (I'm not sure if that's been observed, but I just wanted to say that strong fields can be important too)
So in a nonuniform field such as the sun, a very fast particle also needs to take variation of spatial curvature into account, it's not just an effect for light. In a uniform field, there isn't anything to take into account, so no extra deflection for light or for fast particles. And those effects are about variation of the curvature from place to place, so they strictly go beyond the equivalence principle which is about small enough regions that you ignore variations, if you have to take those variations into account, then you need more than just the equivalence principle. The additional deflection from the variation is an effect in addition to the equivalence principle. And there are many competitors to General Relativity that have an equivalence principle but disagree on the additional deflection (see Clifford Will's book), so it's definitely a real thing. It's just not a thing you have to worry about in a uniform field.