Add a resistor ~10K between 'G' and 'T1' otherwise the gate is left floating when the MOC3023 is turned off. Also ensure you are getting enough gate current through the 1K8 resistor, it would be worthwhile following the data sheet of the MOC3023 which shows a recommended schematic.
The mains input is on T2 and the load output is on T1. Is this you had in mind about the 10K resistor? Add it between gate and load output? By the way, does the order of T1 and T2 makes any difference? It should the same, isn’t it?
You should not cross T1 and T2, they are different inside the triac, they have a PNPN construction with the gate one junction from the end, not in the middle.
Yes, adding the resistor between T1 and G according to your original schematic is what I meant and yes, I suggest you use the schematic you show from the data sheet for best reliability.
What is your load?
You said you were using three triacs to drop 220V to 150V with a 40VA load, that is only about 0.2A but the sine wave will be seriously distorted so an inductive load may try to draw considerably more.
That should be fine.
Use 0.5W resistors, when the MOC is turned off the current is very small so almost no power is dissipated in the resistors, when it is turned on, the voltage across the triac is only a few volts so again the current is quite small.