How do you, analytically, show you are not using too many features?
My approach would be quite similar to yours with a baseline, maybe just a bit more general:
Assuming it's practical (i.e. the training process is not too costly), you could train/test multiple models with various number of features, e.g. 10%, 20%...,100% of the features. For every subset you use an appropriate feature selection method, preferably something like genetic algorithm but it might be too costly. If it's not possible a simple individual feature selection method, e.g. using information gain, but it's likely not to be optimal. Once all the models have been trained, tested and evaluated, a plot of the performance as a function of the number of features should (hopefully) show a curve which increases less and less but never reaches the plateau. If it does reach the plateau before your chosen number of features, it means that you could actually cut down the number features.