Thanks for the clarification. In that case, it seems to me that AudioPlayHead::getCurrentPosition() is returning an erroneous value in the circumstances I describe here:
When I follow the steps in my description there, the VST3 version of the plugin shows me time elapsed since I turned on my computer, rather than time elapsed from the start of the project.
Besides the possibility of a JUCE bug, it might also be some misunderstanding on my part, as I’m still very new to JUCE, and don’t know enough yet to determine exactly why I’m seeing unexpected results in the VST3 plugin.