2.47x? Hmmm. Don't have any ideas. Just some random thoughts (brainstorming).
Might possible be bpfo on a six-ball bearing (are these ball or sleeve bearings?).
Here is one thing I would suggest. Put your spectrum on a log scale (so you can see very tiny peaks) and see if this peak fits into a harmonic series as either a harmonic or a fundamental.
For example you might see 0.5x, 1x, 1.5x, 2x, 2.5x (large), 3x etc. That might indicate some looseness with the 2.5x magnified by resonance.
You might see 2200cpm, 4400cpm, 6600cpm, 8800cpm, which would seem to indicate fundamental frequency of 2200cpm, perhaps consistent with ball bearing problem. Or if this is sleeve bearing, perhaps worse might indicate impacting on the shaft shoulder (should not occur if coupling gap is set to maintain motor near mechanical center).
If no evidence of impacting (no harmonics above or below), then I would go more with your idea possibly magnetic center problem hunting and interacting with a flex coupling.
Or the load may induce some axial movement which through the flex coupling pushes the motor off-center slightly and some kind of interaction grows to large shaft movement. We have such a case one horizontal sleeve bearing motor drives pump through Thomas Shim Pack coupling. At high pump flows everything is fine. At low pump flows you can see the motor shaft move up to 1/8" at fairly low frequency perhaps 2-3hz. Interesting that the motor can move so much when pump thrust bearing only allows approx 10 mils movement. Clearly the movement at the pump is being magnified by an axial resonance of the coupling/system.
In your case with higher frequency perhaps put a strobe on shaft and check for axial movement. While you're at it put the strobe on the coupling.
Perhaps there is some resonance on the end bells. Might be checked with a bump test.
By the way, is there any load attached to this machine? What type? Any belts or gearbox attached to this machine by changce (those can generate strange frequencies).
It might be interesting to check if the vib exists on both ends of the motor. Also is it in phase across the motor. And does the frequency show on the pump or whatever load?