Let's review your findings and the suggestions so far, and look at their implications.
0) The fan is a large between bearings fan, directly driven. The DE bearing should be the axially locating bearing. The DE bearing is pedestal mounted and the pedestal appears to be separate from the casing.
1) You have low radial vibration at all points on the motor and fan and low axial vibration at all but the fan DE bearing.
2) At the Fan DE bearing the 1x is dominant.
3) There is a 180 Deg phase difference axially across the pedestal left to right.
4) There is an erratic phase change axially between the motor DE and the fan DE bearings.
5) there is a 115 deg axial phase change between fan bearings
6) Axial vibration amplitudes at the fan DE bearing are not steady, but change appreciably from reading to reading.
7) A previous problem with high casing vibration led to the casing being stiffened.
Suggestions so far:
Unbalance - Unlikely to be the root-cause. Whilst the rotor of a fan of this type is axially offset from the centre of the shaft span, hence unbalance will generate some axial vibration, the radial vibration will normally be much higher. So, as the radial vibration is low, I would expect the unbalance forces to be modest at best. This would be the case even with significant couple unbalance. If the force generating the vibration is unbalance, this implies axial resonance of the DE bearing pedestal.
Flow Turbulence - again, why is the flow turbulence generating such high 1x axial vibration? Flow turbulence generally creates a broad-band non-synchronous excitation. For it to generate high axial 1x vibration at the pedestal, the pedestal would have to be axially resonant.
Motor running off the magnetic centre - If the motor has plain bearings, this is a possibility. In a motor with plain bearings, the DE bearing axial clearance is quite high and the fan DE bearing would be the locating bearing, if the coupling is axially stiff, the force would be transmitted to the fan DE bearing. If, on the other hand, the motor has rolling element bearings, the force would be felt at the motor DE bearing.
Misalignment / Locked coupling - Unlikely - the symptoms don't match - the motor axial vibration is low and the phase change erratic. It is possible if the motor has plain bearings as axial shaft forces may not couple well to the motor bearing housing.
Axial resonance of the pedestal - as Ron has suggested. This is likely in my opinion - the erratic vibration trends and large difference between the Fan DE axial and other readings support this. Either do a bump test or look at the spectrum in a log-amplitude format and look for a raised noise floor in the vicinity of the 1x peak. A pedestal resonance may be caused by a crack, by insufficiently tightened pedestal holding down bolts or improperly flat mating faces on the pedestal. A mini-ODS on the pedestal and floor would help identify this. Note, As I believe the pedestal and casing should be separate you might want to check the two are not bridged in some way.
I would also look strongly at 1 further possibility:
A cocked bearing - The Fan DE bearing is a spherical roller bearing and so should overcome this, however I have personally seen very similar symptoms earlier in my career on a larger ID fan than this in Blast Furnace cast-house floor extraction service. On opening the bearing housing we found a taper-bore bearing had been installed on a parallel shaft without the taper collar!
Hope this helps