Modeling time in multilevel logistic regression

Question

I conducted an experiment in which participants listened to sentences while looking at pictures about the sentences on a computer screen. Whether at a given time point a participant looked at the left half of a picture or the right half of a picture was recorded via an eye-tracker.

The study had a 2 by 2 within subjects and within items design. If time was not an issue here, I could use the model below (using R code). (Here, I assume varying random intercepts and random slopes for both subject and item.)

lmer(look ~ iv1 * iv2 + (1 + iv1*iv2 | subject) + (1 + iv1*iv2 | item), 
     family = "binomial", data=data)

However, given that participants listened to sentences each of which lasted a few seconds, where they looked at (left vs. right) would vary across time. So one way to model time might be to include time as a covariate (it may even be necessary to natural polynomials):

lmer(look ~ iv1 * iv2 + time + (1 + iv1*iv2 | subject) + (1 + iv1*iv2 | item), 
     family = "binomial", data=data)

But things get complicated since (1) it is possible that time interacts v1 and v2 and (2) I probably need to somehow model time in the random effect terms. An additional complication is that eye-tracking data is fairly large. The particular set of data that I am working with currently has 5 million rows, so running even the simplest multilevel logistic regression can be fairly time consuming.

So my question is, given my design, what would be a good way to model time.