As an example, I can't use pidl to build code for projects that use the Apache license. (seems to be a likely need, involving the ncacn_http RPC-over-HTTP nonsense or WebDAV) Fortunately 4-clause BSD code isn't as common as it once was, but any project which depends on such code is also blocked from using pidl and the associated libraries.
The FSF uses a special exception for libgcc, and also for the bison code. That would be a good start.
In general the LGPL is an excellent choice. I used it on the Linux /bin/ps code, in part because I might want to make a standard system library out of it. Since you never know what might need to go into some future system library, the LGPL is a safe bet.
Multi-licensing is even better: GPL with libgcc-like exception, LGPL, Apache license, MPL, CC-by-sa, etc. Perhaps, as the SDL (graphics library) project has done, also have an exception or two for embedded systems.
Please bring this up on the email@example.com mailing list, as this will require much broader discussion.
Also, if you can show in more presise terms which free software project would benifit by such a relicencing, it would assist in the dicussion.
Please discuss on the mailing list instead (see previous comment).