If convincing people to use a more structured UI is difficult but they're quite happy giving you all the information you need in their own way, why not just accept the data in the format that they want to give it to you in? It seems like a pretty simple NLP problem - you've got a known set of drug names and contractions, a set of timing intervals and a set of dosages. If they're not bothering to provide some of that information that might be an issue (depending on how well you can rigorously determine and encode the context-specific assumptions that they're making), but if they are providing it all to you like that then parsing your clean data out of the text can be done with extremely high accuracy. Potentially higher than the accuracy of a doctor picking from a set of dropdowns, before anyone says "extremely high isn't good enough for healthcare".
I'm sure it's an avenue you've explored - what's been the major challenge?
It's a statement that comes from knowing a lot about the tools and not a lot about the area in which you're applying them. That applies to a lot of startups, rarely the successful ones, and in this instance it certainly applies to me, and probably most of the readers of this thread.
The purpose of the comment is to offer up the strawman solution so that we can hear more about the interesting part of the problem that means it isn't trivial.
I'm sure it's an avenue you've explored - what's been the major challenge?