What is the effect of gradual increase of speech speed on speech comprehension?
The ability to understand speech at increased voice rates is all about learning. A notable example in this regard is the use of text-to-speech software like Jaws used by blind folks unable to read the written word. Jaws is able to convert text on screen into the spoken word using a speech generator. After people get used to read on-screen content through speech, they are often able (and happy) to increase the voice rate settings to scan over the (often cluttered) computer screens more quickly. A recommended incremental step for Jaws in speech rate is 5%. I have experienced the speech rates deployed by some blind folks and the resulting speech was totally unintelligible to me. 

With regard to the learning curve you describe: I bet that after repeated exposure to higher speech rate settings you wouldn't feel the necessity to start at a slower pace. Assuming you have normal vision, you are probably not too inclined to practice this for hours, though.