If you hold a presentation you don't need to compromise between those. You have the opportunity to think well about what to say and rehearse a lot. There are people whose presentations are "too fluent". I mean they do not grant their audience the shortest of pauses. Don't do that ;)

In the Questions&Answers part it's natural that your wording may become less spot-on. Sometimes you notice that mid-phrase, and may want to correct yourself by the addition of some half-phrase like: "...or <better expression>, rather."

  Tulum:

 In the academic field,  "fluency" and "accuracy" are almost the same thing.

In conversation,  a   very much smaller vocabulary is needed. Errors  do not matter so much.

 In the academic field,  a   far more expansive vocabulary is need;  and particularly 

where written  material is concerned,   accuracy is vital.

    You can achieve both the expanded vocabulary  and fluency (with accuracy)  in

academic writing by  reading in  a  specific subject in  non-fiction. 

If you do readings in mathematics, it is a basic way to develop  a fluency and the necessary vocabulary.  Also,  readings in Geometry  can be of help.  There are many websites for these subject in which one can be taught for free  at the elementary and higher levels. This will develop vocabulary.

Tests on the internet, and in books can be of assistance. 

 If you find a language partner  who will read  over texts with you,  our ability will  rapidly improve.

Watching and listening to videos  concerning academic subject can also help.

 For informal communication, fluency is more important than accuracy, but for formaly communication, lessons or business, accuracy is more important. Different environment different requirement.

Well I guess both are necessary if you want to be very credible and professional. At the College there were Italians professors who were forced to give their lessons in English. In my opinion they screwed everything because even professors who are considered very intelligent (and accurate) they seemed dumb trying to give in English their explanations. So I think that before start teaching in a foreign language you must absolutely be fluently in that language oherwise is better you forget it. 

Hello Moritz Noricus,

Yes, you're right. Thank you very much for your time.