The right way to do this is to use different accents for lowercase and uppercase. You may notice some fonts that do this — Gentium is one example.
Gentium Accents.png
Two periods don’t always work either. The umlaut and dot accent should often be smaller than the period.
The Complete Composites data file is designed to facilitate using different accents for lowercase and uppercase. The low profile accents are defined in the Private Use Area at decimal code-points 57365-57376 with umlaut at 57376. If you define these in the same vertical position as you would normally for lowercase, Complete Composites will use them for uppercase composites instead of the normal profile accents, and position them appropriately. See the Complete Composites Tutorial thread.