What does you GDT look like? parameters? DCR, LP, #turns , µe
It looks like you driving equivalent of 560Ω high 360Ω which is // ( Ciss +Rg) low.
If you made your own then a turns ratio direct from 50Ω transformer could be around 1:3 with 5Vpp drive. Compare bipolar and single sided with DC offset. It is the DC content of your drive that makes the transformer warm.
The high side NPN in your circuit has larger Vce and with the excitation current of your primary and larger Vce of the emitter follower is limited by the impedance of 2pi f L which is affected by saturation and operating frequency and inductance.
The reference design is lacking all these details, which are essential to get good results.