EF25 is a big core for 7W but I guess you need a good layer of insulation. I notice you are driving the mosfet at 7.8kHz 50% duty cycle, so that gives you an on time of 64us, I think you need much bigger magnetic coupler for 7.8kHz, 10 Watt audio transformer spring to mind. Dave, where is the light bulb (Gru) emoji thingy ?
If you are using squarewave voltage drive then use the volt time product to calculate your minimum number of primary turns for a given core and winding size, mathematically you've got five variables which are assumed to be linear and you can translate or arrange them five ways, minimum.
(1) V*t = N*B*Ae, (2) B = V*t/(N*Ae), (3) N = V*t/(B*Ae), (4) t = N*B*Ae/V, (5) Ae = V*t/(N*B), (6) f = 1/2t = V/2*(N*B*Ae) where
B = flux density (T)
V = applied voltage (V)
t = on time (us)
N = number of turns
Ae = effective core area (mm2)
f = switching frequency in MHz at 50% duty cycle
For the known variables
V = 9V, t = 64us, Ae = 52.5mm2 for an EF25 core, B = 200mT, only because it's a good place to start from, then
Nmin = V*t/(Bmax*Ae) = 9*64/(0.2*52.5) = 55 turns. At Bmax = 250mT then Nmin = 9*64/(0.25*52.5) = 44 turns.
From astored energy point of view, assuming you wound the primary with 55 or 56 turns how much energy could you store in say TDK N87 ferrrite, Al for ungapped N87 is 1850nH and at 55 turns that's 5.6mH. Energy stored = 1/2*I2*L and I = V*t/L
Peak current I = V*t/L = 9*64E-6/5.6E-3 = 100mA, Stored Energy = 1/2*L*I2*L = 1/2*0.12*5.6E-3 = 28uJ
Maximum power you could transfer P = operating frequency*stored energy per switching cycle = f*E = 7.8E3*28E-6 = 220mW.
You need to increase the operating frequency and use less turns on the inductor.