Calls for shifting visualization research to general audiences outside of professional contexts have been put forward since the early 2000s, but expanding outwards means contending with a diversity in visualization's communicative purpose beyond transmitting insights from data. After our own experiences studying public-facing visualizations, we sought a set of considerations to help early-career visualization researchers reason through designing empirical visualization studies for the general public that confronts the various ways visualizations are interpreted. We examined literature on guiding paradigms of research, reviewed 73 visualization papers that specify a focus on audiences broader than domain experts, and conducted 15 semi-structured interviews with authors of such papers, to derive the following: (1) a conceptualization of any experiment as 3 elements-casting audience, constructing experimental setting, and projecting audience impressions and interactions into measurable constructs (2) an account of interviewees' aspirations for each element of study design, versus the real challenges that occurred. We detail their approaches to navigate the gaps between aspirations and reality when working with general audiences and summarize them as actionable recommendations. The conceptual framework is intended to help junior researchers scope and outline experimental designs of visualizations "for the masses", while the recommendations provide concrete guidance for putting those designs into practice. The 73 papers are filterable and visualized on our study website, and our code to sample the papers is on GitHub.

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