See attached for a stitched schematic from
here (pdf page 303-305). It's wide. View the image in a separate tab and zoom in if necessary.
Flaming RIFA caps (before the transformer) don't usually kill transformers. They might trip your panel breaker since it's directly attached to the IEC receptacle (see page 263). I believe the FLI box in the schematic houses R1 and C1 since I can't find "FLI" in the component lists. Their use here is only for RFI suppression so you can cut it out temporarily (order 0.047uF class X2 safety cap) and get on with further troubleshooting.
The transformer secondary looks pretty straightforward; one winding with center tap and symmetrical intermediate taps.
The two symmetrical intermediate taps and outer winding feed their own full bridge rectifiers with center tap being GND.
With any troubleshooting exercise, start with confirming that the power rails are within spec. Although you don't know what the transformer secondary taps should be, you can infer that they should be symmetrical since the regulated outputs are. Start with documenting all winding outputs, if any are missing or aren't symmetrical.
I'd disconnect the J1 connector from the board and measure: (multi-meter set to ACV)
(a) pins 1,2 should be double that of 1,3 and 2,3
(b) pins 5,4 should be double that of 5,3 and 4,3
So were you measuring 38VAC between J1 pin 1 (or pin 2) and pin3 (GND)? ie. bridge AC input and GND?
If so, that's the peaks, therefore the VRMS is just 27V (38*0.707) so just 4V above +23V regulated output. This seems reasonable.
If the transformer secondary taps are all available and reasonable then reattach transformer J1 and measure all regulator outputs: +/-23VDC, +/-15VDC, +5/-5.2VDC
What lead you to believe that the transformer was bad? Are you not seeing any activity on the front panel?