As far as I know, it's not about lubrication and it's not a manufacturing mistake. Ticking is really simply always there for some fan models. There's nothing you can do. I guess the solution is to try to find fans that don't have that ticking or anything else that's annoying.
I bet an AIO cooler won't be a solution as you'll still have to find a great fan, and you'll additionally get a pump. That pump also might end up being a headache with regards to ticking or other strange noises, and you won't be able to replace the pump unlike what you can try to do with the fan on the AXP-200.
If you do something awesome with water where you have a single radiator for both GPU and CPU, that seems like it should be great as you replace several fans with just one and the pump?
About fans, the PWM Noctua fans have absolutely no ticking. That's their special feature.
I have a 3-pin fan from Yate Loon that has ticking, so 3-pin fans aren't totally safe.
Overall I have no idea how to make absolutely sure to not get an annoying fan.
I'm guessing the "Prolimatech Ultra Sleek Vortex 140mm" might be very interesting for use on the AXP-200. It's a slim 140mm fan with 120mm fan mounting holes. Here's the website:
On paper it's a lot more quiet (though also lower max RPM) than the TY-14013 on the AXP-200. That's the fan I would try if there's no space for a normal 25mm thick fan.
You might be able to find sound recordings about that Prolimatech fan on Youtube? It might be perfect, but it has ball-bearings. Those bearings make it last a bunch of years longer than normal fans, but it could produce a quiet "sssssssss" sound.
You can check out what I mean with the TY-141 recording on that website I linked to earlier (the TY-141 has ball bearings).