Many thanks to both of you for your answers, which have helped me to see things more clearly, both for modeling this data and for other applications in my field.
Indeed my data do not include a 0 value since the minimum duration is by definition 0.03 seconds. In some similar cases, this minimum duration may represent a larger proportion of the whole.
Before considering ordbetareg, I had thought of using a lognormal (or skew normal) distribution, but this seems less appropriate to take into account the presence of this lower bound. I gave it a try with a gamma distribution that I hadn’t thought of before (thanks @amynang for the suggestion). This distribution fits my data rather well, but not as well as ordbetareg for the lower end of the scale, as can be seen on the pp_check plot zoomed in on the [0;0.2] range below.
I’m hesitating between a hurdle_gamma model on data shifted by 0.3 seconds and therefore relative to the minimum duration which would correspond to the value 0, which does indeed seem a more obvious choice, or keeping ordbetareg on data normalized in percentiles according to the approach proposed by @saudiwin. I think the latter approach is relevant to my research question, since I’m more interested in comparing the magnitude of the effects of different factors on duration than in values in seconds. The values in seconds will only be useful to give an order of magnitude of typical values for the different values of my predictors, but I suppose I can apply an inverse transformation to express the predicted values in the original scale.
In my case it doesn’t make much sense to define a maximum duration in milliseconds for normalizing the data as percentiles, but I can define an upper bound depending on the distribution of the data.
The other reason why I’m more inclined to use ordbetareg is that, from the few tests I’ve made so far, this model seems to me both more computationally efficient and to allow a more direct interpretation of the results than the hurdle models (but as I have very little experience of using these models I may be missing something obvious).