I doubt the speakers and locking are related - they go through different circuits for the most part, and the only place that they meet are at connectors inside the A pillar to connect door loom to vehicle loom.
Though even then, the locking commands are dealt with in the outstation (and microswitch connections from the door latch for manual locking/syncing of key etc) and this talks to the BECM through a serial link over 4 wires. If the other functions in the door all work like locking/unlocking with the key, the window and mirror, then it's unlikely that the issue is related.
Out of interest, is passive immobilisation switched on in the BECM? If it is, then try turning it off and syncing the key in the door. If it is on, then maybe try turning it on, and then syncing the key. There's no rhyme or reason for it making a difference, but I've found a few times now that it seems to get confused and changing that gets the key to sync again. Also worth clearing the RF memory aswell. If the key syncs up, then you can toggle the passive immobilisation again, and it should all be tickety boo
If that doesn't make any difference, then also check to make sure the key in switch isn't sticking (getting IGNITION KEY IN on the dash when it isn't) as that can also cause issues with key syncing.
If none of that works, then the only other think I can do (when I'm home!) is if you are happy to send the BECM and keys, then I can check to make sure the fob code matches what is programmed in the BECM. If the BECM is unlocked, and you can read the fob code, then I could read the transmission from one of the keys with me fob reader and tell you what should be programmed in the BECM.
Also worth checking all the door microswitches and all that (can be viewed on the Faultmate under the BECM inputs) to made sure they are all working properly too.
Hope this helps,
Marty
'06 4.2 Supercharged Black/Cream "Jess" -- Bought April 2021 (NZ)
'01 4.6 Vogue Black/Lightstone "Snog" -- Bought Jan 2012
'99 4.6 HSE Cobar Blue/Lightstone -- Sold March 2009
'95 4.6 HSE Epsom Green/Tan -- Traded June 2008