In many cases you can with LGPL, and you can with GPL if you explicitly add a licensing exception.
Also, regarding "use ... proprietary modules ... to better your program or library": depends on your definition of "better", but if that's one of your goals, then I agree that you don't want the GPL.
> Also, MPL allows static linking, the LGPL doesn't unless you explicitly state it.
The LGPL allows static linking, as long as you provide the means to relink with a modified version.
> For the record, would 'GPL + Linking exception' be incompatible with the GPL and LGPL?
Only in one direction. You can take code under the GPL plus a linking exception and merge it into a GPLed project, but the result will not have the exception, so you can't add proprietary code to the result.
Also, regarding "use ... proprietary modules ... to better your program or library": depends on your definition of "better", but if that's one of your goals, then I agree that you don't want the GPL.