Have a settings option that allows the user to hide all the inaccessible members of an object in the code-completion. From the client's point of view they are hidden anyway, so why display them all and clutter up the code-completion window?
Take the string class, for example. The first usable entry is the 50th, and appears last on the scrollable list of options!
Compare the code completion window in CodeLite to the much more useful code completion window in NetBeans (append appears first!). Screenshot attached.