I don't have a solution for the Elastic Net but @BTD, you might consider using full information maximum likelihood (FIML) instead of multiple imputation (MI) for your multivariate analysis. FIML is the default estimator in the Structural Equation Models platform in JMP Pro when there are missing data, and given that you have repeated measures data, you might want to look at this example of a latent growth curve model (makes less stringent assumptions about the data than RM ANOVA).
As a side note, this article compares FIML and MI and affirms that,
"Our study confirmed well-known knowledge that the two estimators tend to yield essentially equivalent results to each other and to those from analysis of complete data when the postulated model is correctly specified."
HTH,
~Laura
Laura C-S