BA now uses the gates nearer to the lounge (23 to 28) which is handy, avoiding the long hike down to 34 etc. I'd personally want to leave at least 4 to 5 hours, depending on day. Flow control is regular in the evenings and not uncommon to sit for 30 to 60 mins until takeoff clearance to cdmx is granted. As rain will soon be daily that can slow things further.

Honestly, I'd come a day early or even early morning..leave your bags at airport head out to Mexico City's Centro histórico. Have a nice early dinner and head to airport. Amex lounge is probably better than AA lounge, but can't comment as only use the latter.

As an fyi, when things with Mexican airlines don't go well, irrops treatment will be dreadful, so best to build in a buffer