Earlier quoted context omitted.
Keeping JavaScript from constructing high-precision timers is going to be a cat and mouse game. See the "Fantastic Timers" paper. Link to HN discussion: https://news.ycombinator.com/item?id=16080235
Also: if you don’t have high precision timers, you probably could also go and increase the number of guesses to cancel out noise. After all, this is a statistical side channel attack. This will be fun for quite some time.
The attack is already pretty damn slow (1kB/s) in C, if you have to collect a statistically significant sample in JS it might well slow down enough to not really work properly.