OP, cxfan1960 speaks truth above.

CX may very well rebook you immediately if you misconnect. But, since you're not only on two separate tickets but also below MCT, they certainly are within their rights to take their sweet time rebooking you or even telling you to pound salt (although I highly, highly doubt they'll do this. CX is usually quite friendly in these situations even though you're at fault).

Practically 45 mins can easily be done and if you arrive on time you'll almost certainly make it (provided you've already done online check-in. You must do this). This isn't LHR or LAX or some inconvenient airport. But you have no margin for error if your AA flight is even 20 minutes late.

Realistically you'll probably still be okay even if you misconnect. But since presumably you lack status on CX (which helps significantly in IRROPs) - if you were CX DM or GO, for example I'd say don't worry about it - your downside is real, even though remote. Worst case is all the CX flights are full for whatever reason and they're not too sympathetic to you, so you end up on an afternoon flight or worse. EF can help (if other morning flights are full, I'd recommend your course of action even less), but isn't foolproof. For example if a CX flight goes tech or other pax misconnect and had legit connecting tickets, they're going to get prioritized before you. Or if CX needs to ferry crew last minute. Etc.

Your Sapphire will definitely help. But it'd be a lot more in the bag if you were a CX elite, since your major downside would be mitigated. CX bends over backwards for their elites in IRROPs. I still think you'll be fine fwiw, just downside is real. If you have a critical meeting at 12:30pm in SIN I wouldn't do this itinerary.