this is a very typical concern that candidates have when building their case skills. However, it is extremely important that you understand that putting yourself under time pressure while practicing is absolutely counterproductive! You first have to learn the right way of approaching and structuring cases, and time is the last concern you should have here! It is like learning an instrument - you first HAVE TO play much MUCH SLOWER than regular in order to be able to properly learn. Speed will come by itself after some time! If you try to force speed too early, you become sloppy and will never really master it!
Moreover, I can promise you that as long as you come up with a rigorous and compelling approach, focusing on the logic according to which you will answer the precise case question (as opposed to just listing buckets you want to look into), the interviewer will immediately forget about any perception of "slowness" he might have had a minute before!
In the tradeoff rigor vs. speed, prioritize rigor! Speed follows automatically. And as I said, even if you take 3 or 4 minutes to come up with a rock solid approach, this is much better than taking 30 seconds and then only having a half baked and shaky roadmap.