Should I repeat the testing/training split while repeating K-fold cross validation?
The purpose of k-fold cross validation is to fit the model multiple times and average out to results to estimate the model's predictive performance.
If having done 10-fold CV once and got one result and then repeating it again and getting a significantly different result, probably means the number of folds is too low, and the k-fold process isn't capturing the inherent variability in the data sufficiently well.
A better test is to change the number of folds and see what happens to the average and variance of the combined output.