What you describe sounds a lot like the early stages of fan bearing failure. Over time and use as the bearings wear the gap between shaft and bearing bore gets bigger. That gap also depends on the temperature of the bearing system because the metals expand differently. When the fan is cold the gap is larger, and in a worn bearing it is large enough that the shaft "rattles around" in the bearing bore. But as it warms up and the gap narrows, that stops and the fan becomes silent. In the early stages that may take up to a minute, but as more wear happens it takes much longer, and eventually it never stops being noisy. Last stage is total failure that seizes the fan, but that normally takes a couple years to develop that far. Since you plan to change soon, you already have the proper solution in mind. Just wait until you change the fans, anyway.
Regarding your new fan choice you CAN use PWM fans in your system. That is not becasue the SYS_FAN headers are set up right - the manual indicates it is not, and the three SYS_FAN headers all appear to use only the older Voltage Control Mode (aka DC Mode). That Mode is the only way to control the speed of 3-pin fans, so if you are alreay using 3-pin ones and their speed IS under automatic control, then that is what your SYS_FAN headers are doing. So you COULD use 3-pin new fans if you choose to, and (among others) Noctua includes in their line-up almost identical models of the same fan in both 3-pin and 4-pin types. But one of the design items of the new 4-pin PWM fan type is a backwards compatibility feature so that these fans CAN have their speed controlled by any header using the older Voltage Control Mode (aka DC Mode). It is not quite ideal for that fan type, and such fans typically cost slightly more, but it DOES work.
The number of pins on a mobo fan header does NOT tell you what Mode it uses. Virtually all mobos today are using 4-pin headers because you CAN plug either fan type into such a header, but the the electrical signals from the header could be any of four types:
- Header uses only the older Voltage Control Mode, and CAN control the speed of both fan types because of the backwards compatibility feature of PWM fans (this appears to be what your mobo does);
- Header uses only the new PWM Mode which cannot control the speed of a 3-pin fan - it will always run full speed - but can control speed of a 4-pin one;
- In BIOS setup you have an option to configure the header to use either one Mode or the other so that you can set it to work with whichever fan type you connect; and,
- Fan header can do either MODE type and claims that automatically it will detect the fan type connected and switch its Mode to match.
Note that it is possible (and I'm sure this was done several years ago by a few mobos) to claim the "automatic configuration" feature (4 above) while actually only doing the "DC Mode only" (1 above) because even a 4-pin fan WILL be speed-controlled and you would not notice the difference unless you try to use them a little differently.
Also note that, because the two fan types require different Modes for ideal control, you should plan NOT to mix the two types (using a Splitter) on the same header. Keep different types on different headers and configure each header to suit the fan(s) connected to it.