Goal of LGPL is to protect freedom of developers to modify code of a library (e.g. to improve it, fix bugs, fix incompatibilities, port to new hardware, etc.) shipped as part of proprietary application. This freedom is important for developers of niche OS'es. This protection works, because of hard consequences for proprietary code in case of license violation: proprietary code must be released under GPL then.

MPL doesn't protect such developers, but it "forces" contribution of changes back to original code. In reality, it's ignored.

Header-only library cannot be compiled as separate library, so requirements of LGPL cannot be met by proprietary code.

That would probably do what you want because it applies on a per-file basis and not to the entire program, but make sure you read the MPL FAQ and the fine print before making such a change: https://www.mozilla.org/en-US/MPL/2.0/FAQ/

Yes, MPLv2 does what you want. Consider that it's also used by Eigen. I strongly advocate for MPLv2 for math style libraries.

It might be better to simply switch to the LGPL v3 or later, since that explicitly addresses header libs.

If you can't use the object files to rebuild another version of the program with a modifier version of the library then no that probably wouldn't be compliant. In that case you would probably have to modify the library so it's not inlining every function. (Disclaimer: IANAL)