First of all, FORGET THE (L)GPL. ALL CODE IS DUAL-LICENCED.
So if it comes from Oracle/OO it's ASL. If it comes from LO, it's MPL. (The (L)GPL is irrelevant, because if the code is dual-licenced, you can use the other licence instead.)
So, because Apache distribute as source, and the MPL merely requires that any MPL source files (and any modified MPL source files) accompany the executable - at least as I am led to to understood the MPL - then there is no problem mixing ASL and MPL code so long as the MPL source accompanies the binary.
Given that, you don't even need to relicence!
That was my point about "Apache CAN but WON'T". They CAN take LO code if they so desire. But if they insist on relicencing, then they WON'T take the code.