So are you saying that I should still try and use the Vgs = 3.7V & 150mA quiescent current? just that I have to find a heat sink good enough to make that work?
Or I can use the Vgs = 3.4V & 34mA quiescent current. In both cases yes I am aware I need a heatsink.
I have attached the heatsink I am considering using it has a thermal conductivity of 10.21C/W

Unfortunately, these transistors on a current of 35 mA have a low cut-off frequency and at high frequencies there will be a lower gain. It is possible to stabilize (partially) the current by putting the resistors in the sources and shunting them with ceramic capacitors. Instead of a Zener diode, I tried to use successively connected LEDs that need to be glued to the transistor (for thermal feedback), but then there is a difficulty in setting the current. This is a more competent solution, but then you have to dramatically complicate the power supply circuit of the valves. LEDs are much worse stabilizers than a zener diode. Here is my last, simple upgrade. It allows you to more smoothly change the current and reduce the harmful effects of reducing the threshold when the transistors are heated.
Pay attention to the changes in the scheme. Resistors at the source should be non-inductive (almost).

 

What about using a high power off the shelf amplifier and then boosting up the voltage with a transformer?

A ten-watt broadband transformer is very difficult to manufacture. It is much easier to introduce thermal feedback and complicate the scheme.