Change score an independent variable in mixed model

I have an (ordinal) outcome measured at two time points, baseline and year 1. My colleague is interested in how our exposure variable is associated with the outcome after adjusting for a number of covariates captured at baseline.

However, our exposure variable is a percentage change from baseline to year 1 (percent weight lost, calculated as ((wt_y1 - wt_baseline)/wt_baseline) * 100, and I'm having trouble justifying whether it is statistically sound to use a mixed model to address the research question. My model takes the following form in R syntax:

y ~ x + time + x*time + covariates + (1 | subject)

My data is currently set up in long format, with 2 observations per subject. I'm essentially carrying the exposure variable "backwards," since technically the percentage change exposure should only exist at year 1...but is this even ok to do? We carry the baseline covariates forward, but I haven't seen carrying variables backwards. For example, the data looks like this:

ID x time gender y ...
1 20 0 male 2
1 20 1 male 2
2 5 0 female 1
2 5 1 female 1

I had various discussions with a senior statistician, but we both seem to be stuck. Also, I'd like to add that we're using cumulative link mixed models since the outcome is ordinal. Mixed models seem like the way to go since missing data is readily handled during model estimation, but I'm not sure if we can run them for our scenario.

If anyone has any input or insights, I'd deeply appreciate it!