That’s an interesting discussion. I included partial pooling of participants in my first model, as a varying intercept. However, I’m not completely convinced about the appropriateness of that approach. The problem I see is that when you include participants in the model, you include them as a variable. The model, however, already has a variable measuring worry. If worry affects participants in such a way that they answer faster or slower, then we have a chained causal relationship. So, worry influences participant and participant causes RT; if I condition on participants, then the effects of worry can get blocked or obscured (i.e. parameters pushed towards zero). It may be argued that the variable/levels of participants may also capture effects of other unobserved variables, which are not necessarily related with worry. In that case, it is still uncertain what those relationships are, and many if not most of them would not be of interest for present questions. If this reasoning makes sense, adding participants into the model would at best create additional ‘not quite informative’ uncertainty, and at worst could create multicollinearity issues which end up obscuring the effect of interest. I may be wrong on this, but I cannot come up with a more compelling argument for keeping participants in the model.
Regarding your second point. Although it does not answer to the question about the appropriateness of the distribution, I think you’re right, it wouldn’t get any easier. However, trying to address the problem is still possible and may be worth it in some cases, even if just a partial solution is reached.