If in the LTspice sim, you put a voltage source equal to the output voltage in series with the current source that is the load (below it is best), the load's dissipation will be almost exactly equal to that of a LM7xx regulator passing the same current (neglecting the regulator's quiescent current). You can then alt-click the current source to plot its dissipation, and ctrl-click the resulting trace legend to calculate the average power.

Of course, that only helps if you know the FY6600's current consumption on each rail - but you can measure that with the existing PSU, and your new transformer's output voltage when loaded with a RMS current of 1.6 times the DC current, or with the actual DC current after the bridge + reservoir capacitor.

*Taking the example of your nominally 18V RMS @100mA transformer, its nominally 230V in so at 240V the output voltage will already be 18.8V, nearly 5% high. You measured its no-load voltage as 25V. At 80mA RMS, for 50mA DC out, I estimate the voltage (by interpolation) will be 20V RMS. Plugging that into the sim in place of the 9V the source Vac was set to, changing the cap to 100uF, decreasing Iload to 50mA and adding a 12V source so the regulator dissipation can be plotted, I get 645mW for the regulator dissipation. That does *NOT* include the power dissipation due the the quiescent current (from In to Gnd), which is another 126mW, so the total LM7812 dissipation at 50mA load current with 20V RMS in will be 0.77W. Revised sim for attached.*

Add up the expected regulator dissipations for all the rails, and the result should be close enough to choose a heatsink size. I strongly suspect you'll need an external heatsink, or fan cooled as I expect you'll have a worst-case dissipation of not much under 10W

Don't put any fan on the 5V rail as it makes the regulator dissipation problem worse. The full wave rectified 9V rail should be in the right ballpark to run a 12V fan a bit slower than normal.