> 5W transformer ...45mA, ..., but for a current of 90mA, the trafo is then rated 20W
Yes. These *SE irons are really 5K impedance. Same impedance, double the current, you imply double the voltage, thus _four_ times the power.
In fact you won't change the supply voltage, won't get double voltage. You will cut the impedance in half, double current, same voltage, double power.
The *SE irons are targeted at 5K but are also workable at 2.5K or 10K. So you have your half-impedance.
What I would expect to work: 125DSE. Yes, it is rated 70mA. If you flow 90mA, the inductance will drop. But you do not need full inductance, since you are working at lower impedance. Also you are not expecting full 20Hz Hi-Fi response; guitar is usually better with some iron-strain in the lowest notes.
No, the 125DSE will not "burn up" at 90mA. The DC resistance is small, the DC heat is well inside what a 2x3" core will shed.
Alternatively, look for "super Champ" OTs rated for either 6V6 or _6L6_ and typically 8K/7K and 4K/3.5K nominal impedance. Your two-EL84 is pretty-near one 6L6 in terms of horsepower and loading.
JFYI: two tubes parallel is "dumb" because with two tubes you "could" run push-pull, use half the iron and half the power filtering and lower distortion. Push-Pull is such an "obvious" win-win-win that very few commercial amps were ever built paralle-SE. (Yes, guitarists are different.)