Triple crossover study and multivariate model with paired data


I would like to analyze data from a triple crossover study.

Same population received same drug (or placebo) three times a day with randomly changing the time of taking the drug (morning, noon, evening). In the end, all patients went through all drug regimes and we are dealing with paired observations.
I would like to compare different regimes of drug ingestion and their effect on certain blood parameter (i.e. hemoglobin level) while controlling for other factors/covariates (age, sex, comorbidities, other blood parameters…).

To check if there are differences in three regimes regarding single parameter (i.e. hemoglobin level), paired measures ANOVA would provide an answer.

To adjust for covariates, I would need to build a multivariate linear model, but I’m not sure how to appropriately include different variables - which variable should be set as a dependent variable (there are three rows/variables for each parameter).
1. One solution that comes to my mind is to treat all data as unpaired (independent) and set-up a model with hemoglobin level as a dependent variable and with dummy variables representing drug regimes. However, this seems wrong because I’m dealing with paired data.
2. Other solution that comes to my mind is to create two models. Morning drug regime is considered as a standard, therefore I could create two models with noon and evening data separately. This would make it a bit easier as I can represent all repeated-measure parameters as differences between them. But should I adjust obtained p values then and consider findings statistically significant with lower p value threshold?
3. In line with second solution, I can create a series of ANCOVA models for different parameters with i.e. regime specific hemoglobin as independent variable and adjust for standard (morning) values and other covariates.

Essentially, I would like to show there are no differences between three regimes of drug ingestion regarding hemoglobin and other parameters.
Please suggest which approach would be the best one. All comments are welcomed.