I unfortunately do not know of any successful short video interview answer links (though I will tag [USER=36740]@Amma Usman[/USER] and [USER=36738]@Ram Sabaratnam[/USER] in case they do), but I completely emphasize with your struggles. Having to respond to "loaded" VI questions (which in fact include 2 or 3 broad sub-questions) is very difficult in such a short amount of time. I think the only way to do so is to sacrifice both the depth and the breadth of your answer. Your can limit breath in the way you mentioned, by mentioning only one point instead of your usual two or three for each sub-questions.
You can then also limit on the depth of explanation of each point. For instance, for a 'why the firm' point, say you would normally go on an elaborated narrative as to how your interest in a given practice area originated, how you went about exploring it, how you then realised what are its substantive features that differentiate it from other practices and also attract you, and then explain who the given firm is a market leader in the practice area and is better than its rivals. Now, considering the time constraints and other questions you have to address, you should instead simply state something like 'The main reason I am attracted to your firm is it's strong X practice area, which is demonstrated by their Chambers and Legal 500 recognition. I am attracted to it because of Y (state distinguishing feature in a few words), as illustrated by Z experience (state the basic subject matter of the experience in a few words)'. This way, you should be able to formulate your point in 15-20 seconds.
Finally, I understand how this type of answer may feel unconvincing and underdeveloped. But given the time constraints, you do not have much choice, just as other candidates won't. Thus, the recruiters reviewing your application will adjust their expectations based on that. I think your answer will be fine as long as you (i) have at least one decent substantive point for each sub-question and (ii) are quite clear when stating the relevant motivation in short form.