ok I see the schematic now, maybe it was a glitch on my end
so we're talking single ended then?
Just for cleanliness, you can skip the heater windings and just have them go to "X", and mark the 6.3v winding on the transformer appropriately. Have a gander at some old schematics and you'll see that. Also might help to draw the 12ax7 as two halves, one per-channel. Or just draw one channel and note it as "one channel shown" since the other one will be identical.
anyway, the screen grid must be connected to something at all times. Looks like you're using a switch to disconnect it from a screen tap on the transformer, but it doesn't switch to anywhere else. You get basically 3 options, tied to the plate to put it in triode mode, to an output transformer tap for ultralinear mode, or to a DC power source for pentode mode. Its usually a good idea to have a 100-ish ohm resistor right at the screen to act as a supressor too.
Output tube cathode resistor is typically bypassed to ground with a cap, something in the 100uf range should work. With no bypass cap you have local feedback which can help with frequency response, but it significantly reduces gain and also makes for effectively higher output impedance on the tube. There is no global negative feedback loop here, so output impedance will already be high. I'm a fan of GNFB but it gets a lot more complex to make stable. At a minimum I'd consider some plate to grid or Schade feedback to help flatten things out. The RH84 design uses this if you want to see an example of it. Its just a resistor from output tube plate back to the output tube grid.
the resistor to ground off the plate is not needed. The load is the transformer impedance. With a 5.3k and a 5k trafo you're somewhere around 2.6k of plate load which is too low for an SE 6v6. Its also going to throw away half the power in the resistor, and single ended you're only making about 4 watts at the plate, and approx 80% of that at the speaker terminals.
picky note, but it looks like the plate and cathode are internally tied. Its the suppressor that goes to cathode. Guessing thats just a glitch in the schematic model though.
Power supply doesn't work as-drawn. Tube plates run on high voltage DC and you have no rectifier here. Heater is fine as AC. SInce its not a center-tapped transformer you're looking at a bridge rectifier. If you want to model supplies, this is a handy program to do it
http://www.duncanamps.com/psud2/
so on to ballparking stuff for the output stage. Since you're looking at a 5k transformer, I'll just assume that you're looking at the 250vdc column in the 6v6 datasheet
https://frank.pocnet.net/sheets/127/6/6V6GTA.pdf
so we're on the same one here
this wants 250v plate and screen
-12.5v of grid bias
45ma of plate current
4.5ma of screen (grid #2) current
from this we can work out a cathode resistor. Cathode current is sum total of all tube current, so at idle 49.5ma. We need 12.5v of bias, and Mr Ohm tells us that 12.5 / 0.0495 = 252 ohms of cathode resistor at 0.6 watts dissipation, or 250 2w since thats a part that exists and gives us plenty of operating margin.
Bias is just difference from grid to cathode. For class A operation cathode resistors work perfectly fine and its dead simple. Just need to reference the grid to ground somehow. Datasheet allows us 500k max as the grid resistor in cathode bias mode.
plate voltage is also measured relative to cathode, so you'd need 262.5 volts plate to ground.
don't worry about getting it absolutely dead-nuts, tubes are pretty forgiving so anything +/- 15% will function just fine. Keep the tube heaters within 5% though.
