LGPL should only pose a problem if you explicitly want your program to be used with non-free software. And then only if said non-free software doesn't give you a way to rebuild it yourself, should you want to modify the LGPL program. (So not a problem for open-core or public-source projects, either.)
If, for some reason, you insist on allowing static linking for all the projects, I think the MPL allows this. (People often seem to think of the LGPL, but it's not the only weak-copyleft licence around.)
Otherwise, when releasing your project under GPLv3+, you don't have to put blind faith into the FSF; you can designate a proxy which will decide whether the new version should be allowed for your project or not. This proxy can be yourself, or it can be a different organisation you choose to trust. Plus, I'm pretty sure the GPL allows you to make linking exceptions of your liking.