I can't answer this from the technical perspective of a computational linguist, but I'll try to comment briefly.

Statistically:

When we use a statistical test, we are usually comparing two things. We want to show (roughly) that one is significantly more likely than another. There are much more complex statistical tests, but they all boil down to basically that core. This means that you can either compare two values to see whether one is bigger than the other (whether the difference between them is significant), or whether one value is significantly different from an expected value (e.g., 0 (lack of or observation of an unexpected event), 50% (as in a coin toss), etc.). Since the things you will be comparing will be similar, the comparison is usually unit-less. So in that sense, a log-transform may not be a problem at all. Of course it might mess up the statistical test mathematically, so beware of that. But in principle this may be fine, if you pick an appropriate statistical test. (Note that your intuitions about statistical distributions are irrelevant, so you shouldn't use logs just because you think they look better, but rely instead on a statistical test to tell you whether the results are 'interesting', that is, significant, in a technical sense.)

Regarding frequency and log likelihood for words in a corpus, you probably already know about Zipf's law:

https://en.wikipedia.org/wiki/Zipf%27s_lawBut that partially addresses what you're observing: the relationship between the frequency of words is typically linear on a logarithmic scale. So there may be some sound motivation behind your decision.

The best answer is to consult current sources (e.g., journal articles) doing something like what you're trying to do, and then using the same (or slightly adjusted) methodology for your project. That's how you're likely to get published, at least. If you don't have a good reason for doing something else, that's where to start.

There are various approaches to dealing with frequencies in corpora (that's really the whole field of corpus linguistics!), and there are a number of ways to try to standardize values, find a balance between frequent words and frequent pairings to look at interesting patterns of attraction (e.g.

https://en.wikipedia.org/wiki/Collostructional_analysis), etc. Don't reinvent the wheel if there's already a method out there, and that way your results will be comparable anyway.