I agree with most of what you say about Time Attack, but it’s not meant to be as serious as normal reviewing, which is obviously where we encourage people to spend their time. The game elements (timing and scoreboard) are meant to be fun and encourage a high degree of familiarity with basic vocabulary, not be an accurate assessment of your Chinese level. Therefore, I’m okay with it only partially overlapping with actual ability to write characters.
We have discussed various ways of making it more fair, but this is a continuous spectrum and we decided to draw the line at separating simplified from traditional for now. This has some consequences, of course, such as luck becoming a factor. I currently hold the record for HSk1 simplified and beating that record will require even more luck than I had, which was a lot. I’m pretty sure the record is almost impossible to beat if you get 怎么样, or 谢谢 in the run, because those take several times longer than writing say 几 or 去. Of course, it will also require you to know the characters very well and recall how to write them quickly.
However, I think that luck factor is only there if your goal is to beat the record for HSK1 and maybe HSK2. Higher levels have a much larger range of words, so knowing the words themselves will be much more important than getting lucky (although avoiding four-character 成语 is still nice). You can also focus on beating your own record, of course. Like I said before, this is meant to be a fun way to practise and compete with basic vocabulary.
Regarding your specific suggestions:
Turn off the drawer (or at least, the drawer gesture) for this mode. You’re moving fast, so it’s easier to stroke it out by accident. I don’t want it in this mode (and certainly don’t want whatever penalty it incurs 
)
Good point! I’ve done this many times myself, always by accident.
Ignore the user’s hide reading/definition settings, and always show both. The big problem with production tests is words with similar meanings, and it is frustrating to lose time because you were trying to correctly write the wrong synonym.
Also a good point! Since this is not reviewing, it seems reasonable to override such settings, especially if it’s also a kind of friendly competition. I actually rely on audio quite a bit when doing time attack, so I can see that not having readings at all would be a handicap.
I felt like on some runs I got some pretty complex characters or words, and on others I had better luck. I can’t quantify that, but I definitely saw significant run-to-run variation and I didn’t ever feel like I was going at less than full speed. Trying to normalize for complexity would be nice; a simpler alternative would be to just use a larger test set.
I already discussed this above, but yes, you’re right. I personally don’t think this is an issue since it’s meant to be more of a fun game than a serious assessment of one’s ability. Also, luck would still be a factor. Should we make sure that each run has the same number of characters? Won’t work, because writing two characters in one word is certainly faster than writing two characters in two separate words. Or maybe count the total number of strokes? Same issue there. It seems hard to come up with some easy way of balancing things that is clean and works well. As for the larger set, you already have HSK6, isn’t that big enough? 
Personally, I found it fun to explore the limits of HSK1, but I doubt I will spend any more time on the lower levels. However, I will try to incorporate occasional runs of HSk5-6 in my study routine. I know these characters and words, but I write them so seldom that I need to think too much sometimes. Time attack is a fun way to alleviate that!
