How to use average F1 score in GridSearchCV with OneVsRestClassifier?

Question

I have an imbalanced multi-label classification problem and use the (simplified) code below to determine hyperparameters.

# Pipeline
pipeline = Pipeline([
    ('clf', OneVsRestClassifier(LogisticRegression()))
])
    
# Parameters to test in Grid Search
parameters = {
    'clf__estimator__C': [1] 
}

# Use stratified sampling in each iteration
stratified_k_fold_cv = IterativeStratification(n_splits=2, order=1)
# Optimize for weighted F1-score
scorer = make_scorer(f1_score, average="weighted")

# Grid Search
grid_lr = GridSearchCV(pipeline, parameters, cv=stratified_k_fold_cv, scoring=scorer)
grid_lr.fit(X_train_tfidf, Y_train)

# Print results
print("Best Parameters: {}".format(grid_lr.best_params_))
print("Mean cross-validated F1-score of the best estimator: {}".format(grid_lr.best_score_))

For each of the 15 labels I have binary classes which are highly imbalanced, sometimes towards the 0 and sometimes towards the 1 class. Therefore I would like to, for each label, look at the average F1 score of the 0 and 1 class by using f1_score(average="weighted"). However, when it comes to aggregating the F1 scores of the labels, I would like to build the average (of the 15 averaged F1 scores) again. How can this be implemented? In the make_scorer function I can only specify to use the weighted average once (and think this accounts for averaging the label F1 scores, not for averaging each individual label score).