Hi @ferdinand and @Cairyn, thanks for the answers.
There may be a simpler way to achieve an effect similar to what we want (for example, by caching the world matrix at the time t) but I'm still thinking of alternate ways to be able to access the full mesh information at time t. Caching the full mesh is probably not a good option since we would have to update that cache every time the mesh is changed at any time before t (since this might change the mesh at t). A possible option is to restrict the usability a bit and always evaluate the mesh at time 0, I'm checking if this is something we can do.
Feedback loops could be an issue, but it should never happen that (using the example @ferdinand wrote) P relies on T and T also relies on P in this specific plugin. Also, t should always be a time before the current time, although that might not alleviate this particular problem.
In any case, I'm going to go ahead and mark this as solved, I think I got all the information I need to find a solution.
Thank you both very much for helping me out,
Daniel