Can I ask DESeq2 which variable alone explains which gene's behavior the best?

Imagine I have a dataset of highly periodic gene expression, taken at densely spaced timepoints. I know that the expression is periodic, but different genes have different offsets.

It is trivial to convert my timestamps into a cosine (cos_time = cos(offset + time*pi*2/PERIOD)), so that this new variable is linear with the genes' expressions -- but only with the ones that have a peak at offset.

What if I could have multiple cos_times (let's call them phases) and then ask DESeq2: "OK, which gene's behavior is most linear with which phase?" Barring comparing p-values of each LRT test, is there a better way?

Disclaimer: I know about cosinor, Lomb-Scargle periodograms, ARS, JTK etc, and I know they are likely more applicable in this particular case. I'm interested in whether it is in general possible to ask such a question from DESeq2, even if the variables in question are not periodic. Phase just seemed like the simplest concept to demonstrate this on.

If you have densely spaced time points the using non-linear regression to directly fit the signal to a cosine or sine curve, which would directly produce the offset, would be much simpler. DESeq2 wouldn't be the appropriate tool then, you'd use base R and the nls() function.
~ Condition + sex + phase1 + phase2 + phase3 + ...