What I did was just build a lot of prototypes and then show those prototypes. It is very hard for people to say that something wont work when you have can show it working right there in the presentation.

You can put that prototyping work under "making presentations and documents in preparation for design discussions", because that is exactly why you prototype. Discussions gets much easier when you are well prepared, so when someone asks about performance you can show them benchmarks, if someone asks about alternatives you can show the difference in benchmarks and code complexity etc. A few hours coding can save weeks of meetings discussing these things.