I'd say you could build more subjective metrics into a model to make it account for these sorts of things when applied objectively, but it would be pretty challenging. It would have to make intelligent decisions about when the "light switch" was flipped and also the odds of it remaining flipped. Maybe it's more of a job for training a model with machine learning.That would require some subjectivity in the application of the model. Sure, the model itself is subjective, but at least its application is objective.
Anyway, Torvik's site can make predictions like this on a per-team basis. On the main rankings page, set the start date to the "light switch moment" and note the ranking (e.g. if set to 1/5, Illinois is #6). Now, go to the team page and click on Teamcast. In the box for Projected T-Rank, enter the number noted earlier. Then, scroll down a bit to the bottom of the schedule, and click Submit (under the extra games section). The projected record and schedule (and its expected win percentages) are updated to reflect how the team has been playing since the specified date. This, of course, assumes no other teams improve or get worse over the remainder of the season.
Based on Illinois' performance from 1/5 on, Torvik's overall projection is 21-10 (13-7). The individual game predictions are more favorable, with only four losses: @Purdue (52%), @Iowa (54%), @Rutgers (56%), and @OSU (55%).